Exhibit 10.5

Execution Version

BG MEDICINE, INC.

NON-QUALIFIED STOCK OPTION AGREEMENT

AGREEMENT made as of the 10th day of May 2013, by and between BG Medicine, Inc. (the “Company”), a Delaware corporation, and Paul Sohmer, M.D. (the “Participant”).

WHEREAS, the Company desires to grant to the Participant an option to purchase shares of its common stock, $0.001 par value per share (the “Shares”) as an inducement material to the Participant’s entering into employment as President and Chief Executive Officer of the Company, effective May 8, 2013 (the “Vesting Start Date”), in accordance with the terms of an employment agreement with the Company dated May 8, 2013 (the “Employment Agreement”);

WHEREAS, the Company and the Participant each intend that the option granted herein shall be a non-qualified stock option (the “Option”).

NOW, THEREFORE, in consideration of the mutual covenants hereinafter set forth and for other good and valuable consideration, the parties hereto agree as follows:

The Company hereby grants to the Participant the right and option to purchase all or any part of an aggregate of 460,480 Shares, on the terms and conditions and subject to all the limitations set forth herein, under United States securities and tax laws. Except as expressly provided in this Agreement, no issuance by the Company of shares of stock of any class, or securities convertible into shares of stock of any class, shall affect, and no adjustment by reason thereof shall be made with respect to, the number of the Shares. Except as expressly provided in this Agreement, no adjustments shall be made for dividends paid in cash or in property (including, without limitation, securities) of the Company.

The exercise price of the Shares covered by the Option shall be $1.67 per share, subject to adjustment, as provided in Section 9 of this Agreement, in the event of a stock split, reverse stock split or other events affecting the holders of Shares after the date hereof (the “Exercise Price”). Payment shall be made in accordance with Section 5(b) of this Agreement.

Vesting Schedule: This Option shall become exercisable (and the Shares issued upon exercise shall be vested) as follows provided the Participant is an employee, director or consultant of the Company or of an Affiliate on the applicable vesting date:

provided that the number of Shares vesting on each date shall be rounded down to the nearest whole number, while the number of Shares vesting on the final date shall be the remaining unvested balance of the Shares.

The foregoing rights are cumulative and are subject to the other terms and conditions of this Agreement.

Notwithstanding the Vesting Schedule set forth above or any language to the contrary in this Agreement, if the Company consummates a Change of Control (as defined in the Participant’s Employment Agreement with the Company dated as of May 8, 2013, as amended from time to time), the Option shall become fully vested and immediately exercisable as to all remaining then-unvested Shares, immediately prior to, and subject to the consummation of, the Change of Control.

This Option shall terminate ten years from the date of this Agreement (the “Option Expiration Date”), but shall be subject to earlier termination as provided herein.

If the Participant ceases to be an employee, director or consultant of the Company or of an Affiliate for any reason other than the death or Disability of the Participant, or termination of the Participant for Cause (the “Termination Date”), the Option to the extent vested and exercisable pursuant to Section 3 hereof, and not previously terminated in accordance with this Agreement, may be exercised within three months after the Termination Date, or on or prior to the Option Expiration Date, whichever is earlier, but may not be exercised thereafter except as set forth below. In such event, the unvested portion of the Option as of the Termination Date shall not be exercisable and shall expire and be cancelled on the Termination Date.

Notwithstanding the foregoing, in the event of the Participant’s Disability or death within three months after the Termination Date, the Participant or the Participant’s Survivors may exercise the Option to the extent vested and exercisable pursuant to Section 3 hereof, within one year after the Termination Date, but in no event after the Option Expiration Date.

In the event the Participant’s service is terminated by the Company or an Affiliate for Cause, the Participant’s right to exercise any unexercised portion of this Option even if vested shall cease immediately as of the time the Participant is notified his or her service is terminated for Cause, and this Option shall thereupon terminate. Notwithstanding anything herein to the contrary, if subsequent to the Participant’s termination, but prior to the exercise of the Option, the Administrator determines that, either prior or subsequent to the Participant’s termination, the Participant engaged in conduct which would constitute Cause, then the Participant shall immediately cease to have any right to exercise the Option and this Option shall thereupon terminate.

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In the event of the Disability of the Participant, the Option shall be exercisable within one year after the Participant’s termination of service due to Disability or, if earlier, on or prior to the Option Expiration Date. In such event, the Option shall be exercisable:

In the event of the death of the Participant while an employee, director or consultant of the Company or of an Affiliate, the Option shall be exercisable by the Participant’s Survivors within one year after the date of death of the Participant or, if earlier, on or prior to the Option Expiration Date. In such event, the Option shall be exercisable:

(a) Subject to the terms and conditions of this Agreement, the Option may be exercised by written notice to the Company or its designee, in substantially the form of Exhibit A attached hereto (or in such other form acceptable to the Company, which may include electronic notice). Such notice shall state the number of Shares with respect to which the Option is being exercised and shall be signed by the person exercising the Option (which signature may be provided electronically in a form acceptable to the Company). Payment of the Exercise Price for such Shares shall be made in accordance with Section 5(b) of this Agreement. The Company shall deliver such Shares as soon as practicable after the notice shall be received, provided, however, that the Company may delay issuance of such Shares until completion of any action or obtaining of any consent, which the Company deems necessary under any applicable law (including, without limitation, state securities or “blue sky” laws). The Shares as to which the Option shall have been so exercised shall be registered in the Company’s share register in the name of the person so exercising the Option (or, if the Option shall be exercised by the Participant and if the Participant shall so request in the notice exercising the Option, shall be registered in the Company’s share register in the name of the Participant and another person

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jointly, with right of survivorship) and shall be delivered as provided above to or upon the written order of the person exercising the Option. In the event the Option shall be exercised, pursuant to Section 4 hereof, by any person other than the Participant, such notice shall be accompanied by appropriate proof of the right of such person to exercise the Option. All Shares that shall be purchased upon the exercise of the Option as provided herein shall be fully paid and nonassessable.

(b) Payment of the Exercise Price for the Shares as to which such Option is being exercised shall be made (a) in United States dollars in cash or by check, or (b) at the discretion of the Administrator, through delivery of shares of Common Stock held for at least six months (if required to avoid negative accounting treatment) having a fair market value equal as of the date of the exercise to the aggregate cash Exercise Price for the number of Shares as to which the Option is being exercised, or (c) at the discretion of the Administrator, by having the Company retain from the Shares otherwise issuable upon exercise of the Option, a number of Shares having a fair market value equal as of the date of exercise to the aggregate Exercise Price for the number of Shares as to which the Option is being exercised, or (d) at the discretion of the Administrator, in accordance with a cashless exercise program established with a securities brokerage firm, and approved by the Administrator, or (e) at the discretion of the Administrator, by any combination of (a), (b), (c) and (d) above, or (f) at the discretion of the Administrator, by payment of such other lawful consideration as the Administrator may determine.

Exercise of this Option to the extent above stated may be made in part at any time and from time to time within the above limits, except that no fractional share shall be issued pursuant to this Option.

The Option shall not be transferable by the Participant otherwise than by will or by the laws of descent and distribution. This Option may also be transferred pursuant to a qualified domestic relations order as defined by the Code or Title I of the Employee Retirement Income Security Act or the rules thereunder and the Participant, with the approval of the Administrator, may transfer the Option for no consideration to or for the benefit of the Participant’s Immediate Family (including, without limitation, to a trust for the benefit of the Participant’s Immediate Family or to a partnership or limited liability company for one or more members of the Participant’s Immediate Family), subject to such limits as the Administrator may establish, and the transferee shall remain subject to all the terms and conditions applicable to the Option prior to such transfer and each such transferee shall so acknowledge in writing as a condition precedent to the effectiveness of such transfer. The term “Immediate Family” shall mean the Participant’s spouse, former spouse, parents, children, stepchildren, adoptive relationships, sisters, brothers, nieces, nephews and grandchildren (and, for this purpose, shall also include the Participant). Except as provided above in this paragraph, the Option shall be exercisable, during the Participant’s lifetime, only by the Participant (or, in the event of legal incapacity or incompetency, by the Participant’s guardian or representative) and shall not be assigned, pledged or hypothecated in any way (whether by operation of law or otherwise) and shall not be subject to execution, attachment or similar process. Any attempted transfer,

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assignment, pledge, hypothecation or other disposition of the Option or of any rights granted hereunder contrary to the provisions of this Section 7, or the levy of any attachment or similar process upon the Option shall be null and void.

The Participant shall have no rights as a stockholder with respect to Shares subject to this Agreement until registration of the Shares in the Company’s share register in the name of the Participant. Except as provided in Section 9 of this Agreement, no adjustment shall be made for dividends or similar rights for which the record date is prior to the date of such registration.

Upon the occurrence of any of the following events, the Participant’s rights with respect to the Option, except to the extent previously exercised shall be adjusted as hereinafter provided:

(a) Stock Dividends and Stock Splits. If (i) shares of Common Stock shall be subdivided or combined into a greater or smaller number of shares or if the Company shall issue any shares of Common Stock as a stock dividend on its outstanding Common Stock, or (ii) additional shares or new or different shares or other securities of the Company or other non-cash assets are distributed with respect to such shares of Common Stock, the number of shares of Common Stock deliverable upon the exercise of the Option shall be appropriately increased or decreased proportionately, and appropriate adjustments shall be made, including in the Exercise Price, to reflect such events.

(b) Corporate Transactions. If the Company is to be consolidated with or acquired by another entity in a merger, consolidation, or sale of all or substantially all of the Company’s assets other than a transaction to merely change the state of incorporation (a “Corporate Transaction”), the Administrator or the board of directors of any entity assuming the obligations of the Company hereunder (the “Successor Board”), shall, as to this Option, either (i) make appropriate provision for the continuation of the Option by substituting on an equitable basis for the Shares then subject to the Option either the consideration payable with respect to the outstanding shares of Common Stock in connection with the Corporate Transaction or securities of any successor or acquiring entity; or (ii) upon written notice to the Participant, provide that the Option must be exercised (either (A) to the extent then exercisable or, (B) at the discretion of the Administrator, the Option being made partially or fully exercisable for purposes of this Subsection), within a specified number of days of the date of such notice, at the end of which period the Option which has not been exercised shall terminate; or (iii) terminate the Option in exchange for payment of an amount equal to the consideration payable upon consummation of such Corporate Transaction to a holder of the number of shares of Common Stock into which the Option would have been exercisable (either (A) to the extent then exercisable or, (B) at the discretion of the Administrator, the Option being made partially or fully exercisable for purposes of this Subsection) less the aggregate Exercise Price. For purposes of determining the payments to be made pursuant to Subclause (iii) above, in the case of a Corporate Transaction the consideration for which, in whole or in part, is other than cash, the consideration other than cash shall be valued at the fair value thereof as determined in good faith by the Board of Directors.

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(c) Recapitalization or Reorganization. In the event of a recapitalization or reorganization of the Company other than a Corporate Transaction pursuant to which securities of the Company or of another corporation are issued with respect to the outstanding shares of Common Stock, the Participant upon exercising the Option after the recapitalization or reorganization shall be entitled to receive for the price paid upon such exercise, the number of replacement securities which would have been received if the Option had been exercised prior to such recapitalization or reorganization.

(d) Dissolution or Liquidation of the Company. Upon the dissolution or liquidation of the Company, the Option will terminate and become null and void; provided, however, that if the rights of the Participant or the Participant’s Survivors have not otherwise terminated and expired, the Participant or the Participant’s Survivors will have the right immediately prior to such dissolution or liquidation to exercise the Option to the extent that the Option is exercisable as of the date immediately prior to such dissolution or liquidation.

(e) Modification of Option. Notwithstanding the foregoing, any adjustments made pursuant to Subsection (a), (b) or (c) above with respect to the Option shall be made only after the Administrator determines whether such adjustments would cause any adverse tax consequences to the Participant, including, but not limited to, pursuant to Section 409A of the Code. If the Administrator determines that such adjustments made with respect to the Option cause adverse tax consequence, it may refrain from making such adjustments, unless the Participant specifically agrees in writing that such adjustment be made and such writing indicates that the Participant has full knowledge of the consequences on his or her income tax treatment with respect to the Option.

The Participant acknowledges that any income or other taxes due from him or her with respect to this Option or the Shares issuable pursuant to this Option shall be the Participant’s responsibility. The Participant acknowledges and agrees that (i) the Participant was free to use professional advisors of his or her choice in connection with this Agreement, has received advice from his or her professional advisors in connection with this Agreement, understands its meaning and import, and is entering into this Agreement freely and without coercion or duress; (ii) the Participant has not received and is not relying upon any advice, representations or assurances made by or on behalf of the Company or any Affiliate or any employee of or counsel to the Company or any Affiliate regarding any tax or other effects or implications of the Option, the Shares or other matters contemplated by this Agreement and (iii) neither the Administrator, the Company, its Affiliates, nor any of its officers or directors, shall be held liable for any applicable costs, taxes, or penalties associated with the Option if, in fact, the Internal Revenue Service were to determine that the Option constitutes deferred compensation under Section 409A of the Code.

If this Option is exercised, the Participant agrees that the Company may withhold from the Participant’s remuneration, if any, the minimum statutory amount of federal, state and

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local withholding taxes attributable to such amount that is considered compensation includable in such person’s gross income. At the Company’s discretion, the amount required to be withheld may be withheld in cash from such remuneration, or in kind from the Shares otherwise deliverable to the Participant on exercise of the Option. The Participant further agrees that, if the Company does not withhold an amount from the Participant’s remuneration sufficient to satisfy the Company’s income tax withholding obligation, the Participant will reimburse the Company on demand, in cash, for the amount under-withheld.

Unless the offering and sale of the Shares to be issued upon the particular exercise of the Option shall have been effectively registered under the Securities Act of 1933, as now in force or hereafter amended (the “1933 Act”), the Company shall be under no obligation to issue the Shares covered by such exercise unless the Company has determined that such exercise and issuance would be exempt from the registration requirements of the 1933 Act and until the following conditions have been fulfilled:

(a) The person(s) who exercise the Option shall warrant to the Company, at the time of such exercise, that such person(s) are acquiring such Shares for their own respective accounts, for investment, and not with a view to, or for sale in connection with, the distribution of any such Shares, in which event the person(s) acquiring such Shares shall be bound by the provisions of the following legend which shall be endorsed upon any certificate(s) evidencing the Shares issued pursuant to such exercise:

“The shares represented by this certificate have been taken for investment and they may not be sold or otherwise transferred by any person, including a pledgee, unless (1) either (a) a Registration Statement with respect to such shares shall be effective under the Securities Act of 1933, as amended, or (b) the Company shall have received an opinion of counsel satisfactory to it that an exemption from registration under such Act is then available, and (2) there shall have been compliance with all applicable state securities laws;” and

(b) If the Company so requires, the Company shall have received an opinion of its counsel that the Shares may be issued upon such particular exercise in compliance with the 1933 Act without registration thereunder. Without limiting the generality of the foregoing, the Company may delay issuance of the Shares until completion of any action or obtaining of any consent, which the Company deems necessary under any applicable law (including, without limitation, state securities or “blue sky” laws).

12.1 The Participant agrees that in the event the Company proposes to offer for sale to the public any of its equity securities and such Participant is requested by the Company and any underwriter engaged by the Company in connection with such offering to sign an agreement restricting the sale or other transfer of Shares, then the Participant will promptly sign such

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agreement and will not transfer, whether in privately negotiated transactions or to the public in open market transactions or otherwise, any Shares or other securities of the Company held by him or her during such period as is determined by the Company and the underwriters, not to exceed 180 days following the closing of the offering, plus such additional period of time as may be required to comply with Marketplace Rule 2711 of the National Association of Securities Dealers, Inc. or similar rules thereto (such period, the “Lock-Up Period”). Such agreement shall be in writing and in form and substance reasonably satisfactory to the Company and such underwriter and pursuant to customary and prevailing terms and conditions. Notwithstanding whether the Participant has signed such an agreement, the Company may impose stop-transfer instructions with respect to the Shares or other securities of the Company subject to the foregoing restrictions until the end of the Lock-Up Period.

12.2 The Participant acknowledges and agrees that neither the Company, its shareholders nor its directors and officers, has any duty or obligation to disclose to the Participant any material information regarding the business of the Company or affecting the value of the Shares before, at the time of, or following a termination of the service of the Participant by the Company, including, without limitation, any information concerning plans for the Company to make a public offering of its securities or to be acquired by or merged with or into another firm or entity.

The Participant acknowledges that: (i) the Company is not by this Option obligated to continue the Participant as an employee, director or consultant of the Company or an Affiliate; (ii) the grant of the Option under this Agreement is a one-time benefit which does not create any contractual or other right to receive future grants of options, or benefits in lieu of options; (iii) all determinations with respect to any such future grants, including, but not limited to, the times when options shall be granted, the number of shares subject to each option, the option exercise price, and the time or times when each option shall be exercisable, will be at the sole discretion of the Company; (iv) the Participant’s participation in this Agreement is voluntary; and (v) the Option is not part of normal or expected compensation for purposes of calculating any severance, resignation, redundancy, end of service payments, bonuses, long-service awards, pension or retirement benefits or similar payments.

The following terms, as used in this Agreement, have the following meanings:

“Administrator” means the Board of Directors of the Company, unless it has delegated power to act on its behalf to the Committee, in which case the Administrator means the Committee.

“Affiliate” means a corporation which, for purposes of Section 424 of the Code, is a parent or subsidiary of the Company, direct or indirect.

“Board of Directors” means the Board of Directors of the Company.

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“Cause” means (a) dishonesty with respect to the Company or any Affiliate, (b) insubordination, substantial malfeasance or non-feasance of duty, (c) unauthorized disclosure of confidential information, (d) breach by the Participant of any provision of any employment, consulting, advisory, nondisclosure, non-competition or similar agreement between the Participant and the Company or any Affiliate, and (e) conduct substantially prejudicial to the business of the Company or any Affiliate. The determination of the Administrator as to the existence of Cause will be conclusive on the Participant and the Company.

“Code” means the United States Internal Revenue Code of 1986, as amended including any successor statute, regulation and guidance thereto.

“Committee” means the committee of the Board of Directors to which the Board of Directors has delegated power to act.

“Common Stock” means shares of the Company’s common stock, $0.001 par value per share.

“Disability” or “Disabled” means permanent and total disability as defined in Section 22(e)(3) of the Code.

“Exchange Act” means the Securities Exchange Act of 1934, as amended.

“Survivor” means the deceased Participant’s legal representatives and/or any person or persons who acquired the Participant’s rights to the Option by will or by the laws of descent and distribution.

Any notices required or permitted by the terms of this Agreement shall be given by recognized courier service, facsimile, registered or certified mail, return receipt requested, addressed as follows:

If to the Company:

BG Medicine, Inc.

610 Lincoln Street North

Waltham, Massachusetts 02451

Attention: Chairman of the Board of Directors

If to the Participant:

Paul Sohmer, MD

2125 Quaker Ridge Road

Croton On Hudson, New York 10520

or to such other address or addresses of which notice in the same manner has previously been given. Any such notice shall be deemed to have been given upon the earlier of receipt, one business day following delivery to a recognized courier service or three business days following mailing by registered or certified mail.

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This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to the conflict of law principles thereof. For the purpose of litigating any dispute that arises under this Agreement, the parties hereby consent to exclusive jurisdiction in the Commonwealth of Massachusetts and agree that such litigation shall be conducted in the state courts of Middlesex County, Massachusetts or the federal courts of the United States for the District of Massachusetts.

Subject to the other provisions hereof, this Agreement shall be for the benefit of and shall be binding upon the heirs, executors, administrators, successors and assigns of the parties hereto.

The terms and provisions of this Agreement may be modified or amended by the Company in a manner which is not adverse to the Participant. Any modification or amendment of this Agreement which adversely affects the Participant’s rights under the Option shall not be made without the consent of the Participant.

This Agreement embodies the entire agreement and understanding between the parties hereto with respect to the Option and supersedes all prior oral or written agreements and understandings relating thereto. No statement, representation, warranty, covenant or agreement not expressly set forth in this Agreement shall affect or be used to interpret, change or restrict, the express terms and provisions of this Agreement.

The terms and provisions of this Agreement may be waived, or consent for the departure therefrom granted, only by written document executed by the party entitled to the benefits of such terms or provisions. No such waiver or consent shall be deemed to be or shall constitute a waiver or consent with respect to any other terms or provisions of this Agreement, whether or not similar. Each such waiver or consent shall be effective only in the specific instance and for the purpose for which it was given, and shall not constitute a continuing waiver or consent.

By entering into this Agreement, the Participant: (i) authorizes the Company and each Affiliate, and any agent of the Company or any Affiliate administering this Agreement or providing recordkeeping services, to disclose to the Company or any of its Affiliates such

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information and data as the Company or any such Affiliate shall request in order to facilitate the grant of options and the administration of this Agreement; (ii) waives any data privacy rights he or she may have with respect to such information; and (iii) authorizes the Company and each Affiliate to store and transmit such information in electronic form.

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IN WITNESS WHEREOF, the Company has caused this Agreement to be executed by its duly authorized officer, and the Participant has hereunto set his or her hand, all as of the day and year first above written.

Exhibit A

NOTICE OF EXERCISE OF STOCK OPTION

[Form for Shares registered in the United States]

IMPORTANT NOTICE: This form of Notice of Exercise may only be used at such time as the Company has filed a Registration Statement with the Securities and Exchange Commission under which the issuance of the Shares for which this exercise is being made is registered and such Registration Statement remains effective.

Ladies and Gentlemen:

I hereby exercise my non-qualified stock option to purchase              shares (the “Shares”) of the common stock, $0.001 par value, of BG Medicine, Inc. (the “Company”), at the exercise price of $             per share, pursuant to and subject to the terms of that Non-Qualified Stock Option Agreement dated May 10, 2013 by and between the Company and the undersigned.

I understand the nature of the investment I am making and the financial risks thereof. I am aware that it is my responsibility to have consulted with competent tax and legal advisors about the relevant national, state and local income tax and securities laws affecting the exercise of the Option and the purchase and subsequent sale of the Shares.

I am paying the option exercise price for the Shares as follows:

Please issue the Shares (check one):

¨ to me; or

¨ to me and                                         , as joint tenants with right of survivorship,

at the following address:

Exhibit A-1

My mailing address for shareholder communications, if different from the address listed above, is:

Exhibit A-2