Exhibit 10.5

April 23, 2014

OFFER LETTER

Mr. Gary S. Titus

Dear Gary:

I am pleased to offer you a position with BioCardia, Inc. (the “Company”) as Chief Financial Officer, effective upon your signing of this letter. Your full-time employment with the Company will commence on May 1, 2014. Effective upon commencement of your full-time employment at the Company you will receive an annual salary of $300,000, which will be paid bimonthly in accordance with the Company’s normal payroll procedures.

As a Company employee, you are also eligible to receive certain employee benefits pursuant to the terms of Company benefit plans as they may exist from time to time.

Your target bonus will be 25% of your base salary based upon agreed upon milestones with the board of directors.

Subject to the approval of the Board of Directors of the Company, you will be granted an option to purchase 476,000 shares of the Company’s Common Stock. This option shall vest, subject to your continued employment with the Company, as to one fourth (1/4) of the shares on the one year anniversary of your start date, and as to an additional one forty-eighth (1/48th) of the total number of shares subject to the option at the end of each calendar month thereafter. Details of the price of these options will be provided in your stock option grant and determined by the board of directors.

You should be aware that your employment with the Company is for no specified period and constitutes at will employment. As a result, you are free to resign at any time, for any reason or for no reason. Similarly, the Company is free to conclude its employment relationship with you at any time, with or without cause.

For purposes of federal immigration law, you will be required to provide to the Company documentary evidence of your identity and eligibility for employment in the United States. Such documentation must be provided to us within three (3) business days of your date of hire, or our employment relationship with you may be terminated.

As a condition to your employment with the Company, you will be required to sign the Company’s standard Employment, Confidential Information, and Invention Assignment Agreement.

You have told the Company that your signing of this letter, the issuance of the stock option to you, and your commencement of employment with the Company do not violate any agreement you have with your current employer; your signature confirms this representation.

In the event of any dispute or claim relating to or arising out of our employment relationship, you and the Company agree that all such disputes shall be fully and finally resolved by binding arbitration conducted by the American Arbitration Association in Santa Clara County, California; provided, however that this arbitration provision shall not apply to any disputes or claims relating to or arising out of the misuse or misappropriation of the Company’s trade secrets or proprietary information.

To indicate your acceptance of the Company’s offer, please sign and date this letter in the space provided below, sign the Employment, Confidential Information, and Invention Assignment Agreement, and return them to me. A duplicate original is enclosed for your records. This letter, along with the Employment, Confidential Information, and Invention Assignment Agreement, set forth the terms of your employment with the Company and supersede any prior representations or agreements, whether written or oral. This letter may be executed in any number of counterparts, each of which shall be an original, but all of which together shall constitute one instrument. This letter may not be modified or amended except by a written agreement, signed by the Company and by you.

We look forward to continuing to work with you at BioCardia, Inc.

Sincerely,

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