Exhibit 5.1

Gibson, Dunn & Crutcher LLP   811 Main Street Houston, TX 77002-6117 Tel 346.718.6600 www.gibsondunn.com

April 19, 2018

Concho Resources Inc.

One Concho Center

600 W. Illinois Avenue

Midland, Texas 79701

Re:     Concho Resources Inc.

           Registration Statement on Form S-4

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-4 (the “Registration Statement”) of Concho Resources Inc., a Delaware corporation (the “Company”), to be filed with the Securities and Exchange Commission (the “SEC”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), on April 19, 2018 in connection with the proposed issuance of up to 51,015,727 shares of common stock, par value $0.001 per share, of the Company (the “Shares”) upon the terms and subject to the conditions of the Agreement and Plan of Merger, dated as of March 27, 2018 (the “Merger Agreement”), by and among the Company, Green Merger Sub Inc., a Delaware corporation and wholly owned subsidiary of the Company, and RSP Permian, Inc., a Delaware corporation (“RSP”).

In arriving at the opinion expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of such documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render the opinions set forth below. In our examination, we have assumed without independent investigation the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. We render no opinion herein as to matters involving any laws other than the General Corporation Law of the State of Delaware (including the applicable reported judicial decisions interpreting such laws) (the “DGCL”). This opinion is limited to the effect of the current state of the DGCL and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

In our examination, we have assumed that prior to the issuance of any of the Shares (i) the Registration Statement, as then amended, will have become effective under the Securities

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April 19, 2018

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Act and such effectiveness will not have been terminated or rescinded, (ii) the stockholders of the Company will have approved the issuance of the Shares pursuant to the Merger Agreement, (iii) the stockholders of RSP will have adopted the Merger Agreement and (iv) the other conditions to consummating the transactions contemplated by the Merger Agreement will have been satisfied or, to the extent permitted by applicable law, waived and such transactions will have been consummated.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on behalf of the Company, and upon issuance and delivery thereto pursuant to and in accordance with the terms of the Merger Agreement and in the manner contemplated by the Registration Statement, the Shares will be validly issued, fully paid and nonassessable.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Validity of Common Stock” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP

Gibson, Dunn & Crutcher LLP