REDEMPTION AGREEMENT

Exhibit 10.5

REDEMPTION AGREEMENT

This redemption agreement (this “Agreement”) is executed as of January 29, 2015 by and between InfraREIT, Inc. (“InfraREIT Inc.”) and InfraREIT Partners, LP (the “Operating Partnership”).

RECITALS

WHEREAS, this Agreement is being entered into in connection with the Merger and Transaction Agreement, dated as of January 29, 2015, by and among InfraREIT, L.L.C. (“InfraREIT LLC”), InfraREIT Inc. and the Operating Partnership (as the same may be amended, modified or supplemented from time to time, the “Merger Agreement”), pursuant to which, among other things, InfraREIT LLC will be merged with and into InfraREIT Inc., with InfraREIT Inc. as the surviving entity in the merger (the “Merger”);

WHEREAS, InfraREIT Inc. has filed with the United States Securities and Exchange Commission a registration statement on Form S-11 with respect to an initial public offering (the “IPO”) of its common stock, par value $0.01 per share;

WHEREAS, 6,242,999 limited liability company interests in InfraREIT LLC designated as common shares were transferred to a trust (the “Trust Shares”) for the benefit of the Charitable Beneficiary (as defined in the Merger Agreement) as a result of the operation of certain provisions of Article 6 of the Amended and Restated Limited Liability Company Agreement of InfraREIT LLC, dated as of November 23, 2010 (the “LLC Agreement”);

WHEREAS, pursuant to Section 6.18 of the LLC Agreement, InfraREIT LLC has accepted the offer to purchase the Trust Shares from the Trust and InfraREIT Inc., as successor to InfraREIT LLC, has agreed to acquire the Trust Shares contemporaneously with the Merger in consideration for a promissory note with a principal balance equal to $66,517,480 (the “ES Note”);

WHEREAS, it is contemplated that the Operating Partnership will acquire the ES Note;

WHEREAS, pursuant to Section 4.6.G of the Second Amended and Restated Agreement of Limited Partnership of the Partnership (the “Second Amended and Restated OP Agreement”), which will become effective upon the consummation of the IPO, InfraREIT Inc. shall cause the Operating Partnership to purchase from InfraREIT Inc. a number of Class A Units equal to the number of Trust Shares being repurchased on the same terms and for the same aggregate price that InfraREIT Inc. purchases the Trust Shares; and

WHEREAS, in consideration of the transfer and cancellation of the ES Note, the Operating Partnership desires to redeem 6,242,999 Class A Units (the “Redeemed Units”) held by InfraREIT Inc.

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NOW, THEREFORE, in consideration of the premises and of the mutual promises, covenants, conditions and agreements contained herein, and for other valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties agree as follows:

1. Redemption of Redeemed Units. Pursuant to Section 4.6.G of the Second Amended and Restated OP Agreement, immediately upon acquisition of the ES Note, the Operating Partnership hereby transfers to InfraREIT Inc. the ES Note and InfraREIT Inc. hereby surrenders the Redeemed Units and all right, title and interest therein.

2. Cancellation of the ES Note. InfraREIT Inc. and the Operating Partnership agree that upon transfer of the ES Note in accordance with Paragraph 1, the ES Note shall be deemed cancelled and of no further force and effect and none of the respective parties thereto shall have any right or obligation thereunder or arising from the cancellation thereof and that such cancellation shall constitute full and complete satisfaction of any and all obligations of the Operating Partnership to InfraREIT Inc. with respect to the redemption of the Redeemed Units.

3. Termination. This Agreement shall terminate if the closing of the IPO has not occurred within 10 business days of the date hereof.

4. Entire Agreement. This Agreement constitutes the entire agreement between the parties pertaining to the subject matter hereof and supersedes all prior and contemporaneous negotiations, agreements and understandings of the parties.

5. Binding Effect; Assignment. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and their respective successors and assigns. Nothing in this Agreement, express or implied, is intended to confer upon any party other than the parties hereto or their respective successors and assigns any rights, remedies, obligations, or liabilities under or by reason of this Agreement.

6. Amendment and Modification. This Agreement may be amended, modified or supplemented only by written agreement of each of the parties hereto.

7. Counterparts. Any number of counterparts hereof may be executed and each such counterpart shall be deemed to be an original instrument. A signature delivered by facsimile or other means of electronic transmission shall be deemed to constitute an original signature.

8. Governing Law. This Agreement will be governed by and construed in accordance with the laws of the State of Delaware without regard to any conflicts of law provisions that would result in the application of the laws of any other jurisdiction. Any legal action or proceeding between the parties to this Agreement shall be adjudicated solely and exclusively in the state and/or federal courts in Delaware. Each party irrevocably submits to the exclusive jurisdiction of such courts in any such suit, action or proceeding.

[Signature page follows]

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IN WITNESS WHEREOF, the parties hereto have each executed and delivered this Agreement as of the day and year first above written.

Signature Page to Redemption Agreement of InfraREIT, Inc.