Exhibit 10.5

SECOND AMENDMENT TO

FIRST AMENDED AND RESTATED CREDIT AGREEMENT

THIS SECOND AMENDMENT TO FIRST AMENDED AND RESTATED CREDIT AGREEMENT (this “Amendment”) made as of this 11^th day of June, 2013, by and among CARTER/VALIDUS OPERATING PARTNERSHIP, LP, a Delaware limited partnership (the “Borrower”), CARTER VALIDUS MISSION CRITICAL REIT, INC., a Maryland corporation (“REIT”), HC-2501 W WILLIAM CANNON DR, LLC, a Delaware limited liability company (“HC-2501”), DC-19675 W. TEN MILE, LLC, a Delaware limited liability company (“DC-19675”), DC-1221 COIT ROAD, LLC, a Delaware limited liability company (“DC-1221”), DC-5000 BOWEN ROAD, LLC, a Delaware limited liability company (“DC-5000”), HC-8451 PEARL STREET, LLC, a Delaware limited liability company (“HC-8451”), HC-17322 RED OAK DRIVE, LLC, a Delaware limited liability company (“HC-17322”), GREEN WELLNESS INVESTORS, LLLP, a Florida limited liability limited partnership (“GWI”), HC-1940 TOWN PARK BOULEVARD, LLC, a Delaware limited liability company (“HC-1940”); DC-5150 MCCRIMMON PARKWAY, LLC, a Delaware limited liability company (“DC-5150”), DC-15 SHATTUCK ROAD, LLC, a Delaware limited liability company (“DC-15”), HC-239 S. MOUNTAIN BOULEVARD, LP, a Delaware limited partnership (“HC-239 Owner”) HC-239 S. MOUNTAIN BOULEVARD MANAGEMENT, LLC, a Delaware limited liability company (“HC-239 General Partner”; REIT, HC-2501, DC-19675, DC-1221, DC-5000, HC-8451, HC-17322, GWI, HC-1940, DC-5150, DC-15, HC-239 Owner and HC-239 General Partner are hereinafter collectively referred to as the “Guarantors”), KEYBANK NATIONAL ASSOCIATION, a national banking association (“KeyBank”), THE OTHER LENDERS LISTED ON THE SIGNATURES PAGES HEREOF AS LENDERS (KeyBank and the other lenders are listed on the signatures pages hereof as Lenders, collectively, the “Lenders”), and KEYBANK NATIONAL ASSOCIATION, a national banking association, as Agent for the Lenders (the “Agent”).

W I T N E S S E T H:

WHEREAS, Borrower and KeyBank, individually and as Agent, entered into that certain First Amended and Restated Credit Agreement dated as of November 19, 2012 (as modified or amended from time to time, the “Credit Agreement”); and

WHEREAS, REIT and HC-2501 executed and delivered to Agent and the Lenders that certain Unconditional Guaranty of Payment and Performance dated as of March 30, 2012, as amended by that certain First Amendment to Unconditional Guaranty of Payment and Performance executed by REIT, HC-2501 and DC-19675 dated as of June 29, 2012 and that certain Second Amendment to Unconditional Guaranty of Payment and Performance executed by REIT, HC-2501 and DC-19675 dated as of July 19, 2012, and as ratified by that certain Ratification of Unconditional Guaranty of Payment and Performance dated as of November 19, 2012 by REIT, HC-2501, DC-19675, DC-1221, DC-5000 and HC-8451 (as modified, amended, or ratified from time to time, the “Guaranty”); and

WHEREAS, DC-19675 executed that certain Joinder Agreement dated as of May 25, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, DC-1221 executed that certain Joinder Agreement dated as of August 16, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, DC-5000 executed that certain Joinder Agreement dated as of August 16, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, HC-8451 executed that certain Joinder Agreement dated as of September 28, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, HC-17322 executed that certain Joinder Agreement dated as of November 28, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, GWI executed that certain Joinder Agreement dated as of December 28, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, HC-1940 executed that certain Joinder Agreement dated as of December 28, 2012, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, DC-5150 executed that certain Joinder Agreement dated as of March 21, 2013, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, DC-15 executed that certain Joinder Agreement dated as of March 28, 2013, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, HC-239 Owner executed that certain Joinder Agreement dated as of June     , 2013, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, HC-239 General Partner executed that certain Joinder Agreement dated as of June     , 2013, thereby becoming a “Subsidiary Guarantor” and “Guarantor” under the Loan Documents (as defined in the Guaranty), including, without limitation, the Guaranty; and

WHEREAS, Borrower and Guarantors have requested that the Agent and the Lenders make certain modifications to the Credit Agreement; and

WHEREAS, the Agent and the Lenders have consented to such modifications, subject to the execution and delivery of this Amendment.

2

NOW, THEREFORE, for and in consideration of the sum of TEN and NO/100 DOLLARS ($10.00), and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto do hereby covenant and agree as follows:

1. Definitions. All terms used herein which are not otherwise defined herein shall have the meanings set forth in the Credit Agreement.

2. Modification of the Credit Agreement. The Agent, the Lenders and the Borrower hereby amend the Credit Agreement as follows:

(a) By deleting in its entirety the definition of “Mortgage Note Receivables” appearing in §1.1 of the Credit Agreement, and inserting the following new definition in lieu thereof:

“Mortgage Note Receivables. Mortgage and notes receivable and other promissory notes, including interest payments thereunder, in favor of, or payable to, the Borrower or any Subsidiary which are in, or made by, or payable by, any Person (other than the Borrower or its Subsidiaries) that are secured by (a) a mortgage loan on a Data Center Asset or Medical Asset or (b) a pledge of the equity interest in any entity which directly or indirectly (through the ownership of equity interests in one or more entities) owns an equity interest in an entity that owns a Data Center Asset or a Medical Asset.”

(b) By deleting in its entirety §8.3(j) of the Credit Agreement, and inserting in lieu thereof the following:

“(j) Investments by the Borrower or its Subsidiaries (other than the Subsidiary Guarantors) in Mortgage Note Receivables secured by properties that meet the property type requirements of a Data Center Asset or a Medical Asset; and”

(c) By inserting the following new §8.3(k) into the Credit Agreement:

“(k) acquisition of fee simple interests or long-term ground lease interests in Real Estate by Borrower or its Subsidiaries that meet the property type requirements of a Data Center Asset or a Medical Asset.”

3. Consent and Acknowledgment. Agent and the Lenders acknowledge that the mezzanine loans made by Borrower prior to the date of this Amendment for the projects commonly known as (a) Clear Lake/Bay Area Regional Medical Center, 200 Blossom Street, Webster, Texas 77598, and (b) Walnut Hill Physician’s Hospital, 7502 Greenville Avenue, Dallas, Texas, 75231 are permitted Investments under §8.3(j) of the Credit Agreement.

4. References to Credit Agreement. All references in the Loan Documents to the Credit Agreement shall be deemed a reference to the Credit Agreement as modified and amended herein.

3

5. Consent of Guarantors. By execution of this Amendment, Guarantors hereby expressly consent to the modifications and amendments relating to the Credit Agreement, Guaranty and the Loan Documents as set forth herein, and Borrower and Guarantors hereby acknowledge, represent and agree that the Loan Documents (including without limitation the Guaranty) remain in full force and effect and constitute the valid and legally binding obligation of Borrower and Guarantors, respectively, enforceable against such Persons in accordance with their respective terms, and that the Guaranty extends to and applies to the foregoing documents as modified and amended.

6. Representations. Borrower and Guarantors represent and warrant to Agent and the Lenders as follows:

(a) Authorization. The execution, delivery and performance of this Amendment and the transactions contemplated hereby (i) are within the authority of Borrower and Guarantors, (ii) have been duly authorized by all necessary proceedings on the part of such Persons, (iii) do not and will not conflict with or result in any breach or contravention of any provision of law, statute, rule or regulation to which any of such Persons is subject or any judgment, order, writ, injunction, license or permit applicable to such Persons, (iv) do not and will not conflict with or constitute a default (whether with the passage of time or the giving of notice, or both) under any provision of the partnership agreement or certificate, certificate of formation, operating agreement, articles of incorporation or other charter documents or bylaws of, or any mortgage, indenture, agreement, contract or other instrument binding upon, any of such Persons or any of its properties or to which any of such Persons is subject, and (v) do not and will not result in or require the imposition of any lien or other encumbrance on any of the properties, assets or rights of such Persons, other than the liens and encumbrances created by the Loan Documents.

(b) Enforceability. The execution and delivery of this Amendment are valid and legally binding obligations of Borrower and Guarantors enforceable in accordance with the respective terms and provisions hereof, except as enforceability is limited by bankruptcy, insolvency, reorganization, moratorium or other laws relating to or affecting generally the enforcement of creditors’ rights and the effect of general principles of equity.

(c) Approvals. The execution, delivery and performance of this Amendment and the transactions contemplated hereby do not require the approval or consent of or approval of any Person or the authorization, consent, approval of or any license or permit issued by, or any filing or registration with, or the giving of any notice to, any court, department, board, commission or other governmental agency or authority other than those already obtained.

(d) Reaffirmation. Borrower and Guarantors reaffirm and restate as of the date hereof each and every representation and warranty made by the Borrower, the Guarantors and their respective Subsidiaries in the Loan Documents or otherwise made by or on behalf of such Persons in connection therewith except for representations or warranties that expressly relate to an earlier date.

7. No Default. By execution hereof, the Borrower and Guarantors certify that the Borrower and Guarantors are and will be in compliance with all covenants under the Loan Documents after the execution and delivery of this Amendment, and that no Default or Event of Default has occurred and is continuing.

4

8. Waiver of Claims. Borrower and Guarantors acknowledge, represent and agree that Borrower and Guarantors as of the date hereof have no defenses, setoffs, claims, counterclaims or causes of action of any kind or nature whatsoever with respect to the Loan Documents, the administration or funding of the Loans or with respect to any acts or omissions of Agent or any of the Lenders, or any past or present officers, agents or employees of Agent or any of the Lenders, and each of Borrower and Guarantors does hereby expressly waive, release and relinquish any and all such defenses, setoffs, claims, counterclaims and causes of action, if any.

9. Ratification. Except as hereinabove set forth or in any other document previously executed or executed in connection herewith, all terms, covenants and provisions of the Credit Agreement remain unaltered and in full force and effect, and the parties hereto do hereby expressly ratify and confirm the Credit Agreement. Nothing in this Amendment shall be deemed or construed to constitute, and there has not otherwise occurred, a novation, cancellation, satisfaction, release, extinguishment or substitution of the indebtedness evidenced by the Notes or the other obligations of Borrower and Guarantors under the Loan Documents (including without limitation the Guaranty).

10. Counterparts. This Amendment may be executed in any number of counterparts which shall together constitute but one and the same agreement.

11. Miscellaneous. THIS AMENDMENT SHALL, PURSUANT TO NEW YORK GENERAL OBLIGATIONS LAW SECTION 5-1401, BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK. This Amendment shall be binding upon and shall inure to the benefit of the parties hereto and their respective permitted successors, successors-in-title and assigns as provided in the Credit Agreement.

12. Effective Date. This Amendment shall be deemed effective and in full force and effect as of the date hereof upon the execution and delivery of this Amendment by Borrower, Guarantors, Agent and the Required Lenders.

[SIGNATURES BEGIN ON NEXT PAGE]

5

IN WITNESS WHEREOF, the parties hereto have hereto set their hands and affixed their seals as of the day and year first above written.

[SIGNATURES CONTINUED ON NEXT PAGE]

6

[SIGNATURES CONTINUED ON NEXT PAGE]

7

[SIGNATURES CONTINUED ON NEXT PAGE]

8

[SIGNATURES CONTINUED ON NEXT PAGE]

9

[SIGNATURES CONTINUED ON NEXT PAGE]

10

[SIGNATURES CONTINUED ON NEXT PAGE]

11

[SIGNATURES CONTINUED ON NEXT PAGE]

12

[SIGNATURES CONTINUED ON NEXT PAGE]

13

[SIGNATURES CONTINUED ON NEXT PAGE]

14

15