Exhibit 10.5

FIRST AMENDMENT TO

AGREEMENT AND PLAN OF MERGER

This AMENDMENT TO AGREEMENT AND PLAN OF MERGER (this “Amendment”), dated effective as of May 21, 2012, is by and among USMD Holdings, Inc., a Delaware corporation, UANT Ventures, L.L.P., a Texas limited liability partnership, UANT Acquisition Company No. 2, L.L.C., a Texas limited liability company and a wholly-owned subsidiary of Ventures and Impel Management Services, L.L.C., a Texas limited liability company.

WHEREAS, the Parties previously entered into that certain Agreement and Plan of Merger dated December 15, 2011 (the “Agreement”); and

WHEREAS, the Parties desire to amend certain terms of the Agreement as set forth herein.

NOW, THEREFORE, in consideration of the mutual agreements, provisions and covenants contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto agree as follows:

ARTICLE I

DEFINITIONS

Capitalized terms used but not defined herein shall have the meanings ascribed to them in the Agreement.

ARTICLE II

AMENDMENTS; GENERAL

2.1 Section 1.4(c)(v) of the Agreement is hereby deleted in its entirety and replaced with the following, effective as of the date hereof:

(v) to reflect on Schedule 1.41 the amount of any mutually approved capital expenditures (A) since December 31, 2010 relating to fixed assets of the UANT clinical practice and (B) since September 30, 2011 relating to fixed assets or mutually approved capital contributions of USMD, Ventures/UANT, Impel, and MCNT as set forth in Cells K65, M65, O65, and Q65, including without limitation approved capital expenditures for equipment, building or tenant improvements.

2.2 Section 4.4(a) and (b) of the Agreement are hereby deleted in their entirety and replaced with the following, effective as of the date hereof:

(a) As of the date hereof, the authorized capital stock of Holdings consists of 1,000,000 shares of preferred stock, $0.01 par value, of which no shares are issued and outstanding as of the date hereof, and 49,000,000 shares of common stock of Holdings, par value $.01 (“Holdings Stock”), of which 35,800 are issued and outstanding as of the date hereof. As of the date hereof, up to 964,200 shares of Holdings Stock are reserved for issuance under the Holdings Equity Plan. Except as set forth above or in connection with the UANT/USMD Contribution and the MCNT Merger, no shares of capital stock or other voting securities of Holdings are issued, reserved for issuance or outstanding.

(b) Immediately following the consummation of the Merger, the MCNT Merger and the UANT/USMD Contribution, (i) the authorized capital stock of Holdings shall consists of 1,000,000 shares of preferred stock, $0.01 par value, of which no shares shall be issued and outstanding as of the Closing Date, 49,000,000 shares of Holdings Stock, of which

10,035,800 shares are expected to be issued and outstanding as of the Closing Date and 964,200 shares shall be reserved for issuance under the Holdings Equity Plan as of the Closing Date and (ii) the capital structure of Holdings’ Subsidiaries shall be as set forth on Schedule 4.4(b) hereto. Schedule 4.4(b) sets forth (i) the name and jurisdiction of each Subsidiary of Holdings immediately following the Closing, and (ii) a complete and accurate list of all outstanding securities beneficially owned by Holdings or its Subsidiaries immediately following Closing. Except as set forth above, immediately following the consummation of the Merger, the MCNT Merger and the UANT/USMD Contribution, no shares of capital stock or other voting securities of Holdings shall be issued, reserved for issuance or outstanding.

2.3 Other than the amendments and modifications specifically contained in this Amendment, the Agreement remains in full force and effect.

2.4 This Amendment may be executed in one or more counterparts, all of which shall be considered one and the same agreement and shall become effective when one or more counterparts have been signed by each of the Parties and delivered to the other Parties. Facsimile execution and delivery of this Amendment is legal, valid and binding for all purposes.

2.5 This Amendment shall be governed by, and construed in accordance with, the laws of the State of Texas, regardless of the laws that might otherwise govern under applicable principles of conflicts of laws thereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to Agreement and Plan of Merger to be duly executed by their respective authorized signatories as of the date first indicated above.

Signature Page to Amendment to Agreement and Plan of Merger