Exhibit

Exhibit 5.1

355 South Grand Avenue, Suite 100

Los Angeles, California 90071-1560

Tel: +1.213.485.1234 Fax: +1.213.891.8763

www.lw.com

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October 30, 2018

Four Corners Property Trust, Inc.

591 Redwood Highway, Suite 1150

Mill Valley, California 94941

Re: Four Corners Property Trust, Inc.

Ladies and Gentlemen:

We have acted as special counsel to Four Corners Property, Inc., a Maryland corporation (the “Company”), in connection with the Company’s registration statement on Form S-3 (the “Registration Statement”), including a base prospectus (the “Base Prospectus”), which provides that it will be supplemented by one or more prospectus supplements (each such prospectus supplement, together with the Base Prospectus, a “Prospectus”), filed on December 5, 2016 with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the registration for issue and sale by the Company of (i) shares of the Company’s common stock, $0.0001 par value per share (“Common Stock”); (ii) shares of one or more series of the Company’s preferred stock, $0.0001 par value per share (“Preferred Stock”), (iii) depositary shares, representing an interest in Preferred Stock, (iv) warrants to purchase shares of Common Stock, shares of Preferred Stock or Depositary Shares (“Warrants”), and (v) rights to purchase shares of Common Stock (“Rights”).

This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related applicable Prospectus, other than as expressly stated herein with respect to the enforceability of the relevant securities.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the internal laws of the State of New York, and we express no opinion with respect to the applicability thereto, or the effect thereon, of the laws of any other jurisdiction or as to any matters of municipal law or the laws of any local agencies within any state. Various issues concerning Maryland law are addressed in the opinion of Ballard Spahr LLP, which has been separately provided to you. We express no opinion with respect to those matters herein, and to the extent elements of those opinions are necessary to the conclusions expressed herein, we have, with your consent, assumed such matters.

October 30, 2018

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Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof:

1.When the applicable deposit agreement has been duly authorized, executed and delivered by all necessary corporate action of the Company, and when the specific terms of a particular issuance of Depositary Shares have been duly established in accordance with the terms of the applicable deposit agreement and authorized by all necessary corporate action of the Company, and such Depositary Shares have been duly executed, authenticated, issued and delivered against payment therefor in accordance with the terms of the applicable deposit agreement and in the manner contemplated by the applicable Prospectus and by such corporate action (assuming the underlying securities have been validly issued and deposited with the depositary), such Depositary Shares will be the legally valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

2.When the applicable warrant agreement has been duly authorized, executed and delivered by all necessary corporate action of the Company, and when the specific terms of a particular issuance of Warrants have been duly established in accordance with the terms of the applicable warrant agreement and authorized by all necessary corporate action of the Company, and such Warrants have been duly executed, authenticated, issued and delivered against payment therefor in accordance with the terms of the applicable warrant agreement and in the manner contemplated by the applicable Prospectus and by such corporate action (assuming the securities issuable upon exercise of such Warrants have been duly authorized and reserved for issuance by all necessary corporate action), such Warrants will be the legally valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

3.When the applicable rights agreement has been duly authorized, executed and delivered by all necessary corporate action of the Company, and when the specific terms of a particular issuance of Rights have been duly established in accordance with the terms of the applicable rights agreement and authorized by all necessary corporate action of the Company, and such Rights have been duly executed, authenticated, issued and delivered against payment therefor in accordance with the terms of the applicable deposit agreement and in the manner contemplated by the applicable Prospectus and by such corporate action (assuming the underlying securities have been validly issued and deposited with the depositary), such Rights will be the legally valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our opinions are subject to: (i) the effect of bankruptcy, insolvency, reorganization, preference, fraudulent transfer, moratorium or other similar laws relating to or affecting the rights and remedies of creditors; (ii) the effect of general principles of equity, whether considered in a proceeding in equity or at law (including the possible unavailability of specific performance or injunctive relief), concepts of materiality, reasonableness, good faith and fair dealing, and the discretion of the court before which a proceeding is brought and (iii) the invalidity under certain circumstances under law or court decisions of provisions providing for the indemnification of or contribution to a party with respect to a liability where such indemnification or contribution is contrary to public policy. We express no opinion as to (a) any provision for liquidated damages, default interest, late charges,

October 30, 2018

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monetary penalties, make-whole premiums or other economic remedies to the extent such provisions are deemed to constitute a penalty, (b) consents to, or restrictions upon, governing law, jurisdiction, venue, arbitration, remedies or judicial relief, (c) waivers of rights or defenses, (d) any provision requiring the payment of attorneys’ fees, where such payment is contrary to law or public policy, (e) the creation, validity, attachment, perfection, or priority of any lien or security interest, (f) advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitation, trial by jury or at law, or other procedural rights, (g) waivers of broadly or vaguely stated rights, (h) provisions for exclusivity, election or cumulation of rights or remedies, (i) provisions authorizing or validating conclusive or discretionary determinations, (j) grants of setoff rights, (k) proxies, powers and trusts, (l) provisions prohibiting, restricting, or requiring consent to assignment or transfer of any right or property, (m) provisions purporting to make a guarantor primarily liable rather than as a surety, (n) provisions purporting to waive modifications of any guaranteed obligation to the extent such modification constitutes a novation, (o) any provision to the extent it requires that a claim with respect to a security denominated in other than U.S. dollars (or a judgment in respect of such a claim) be converted into U.S. dollars at a rate of exchange at a particular date, to the extent applicable law otherwise provides, and (p) the severability, if invalid, of provisions to the foregoing effect.

With your consent, we have assumed (i) that Depositary Shares, Warrants and Rights and any related board resolution or officers’ certificate establishing the terms thereof (collectively, the “Documents”) will be governed by the internal laws of the State of New York, (ii) that each of the Documents has been or will be duly authorized, executed and delivered by the parties thereto, (iii) that each of the Documents constitutes or will constitute legally valid and binding obligations of the parties thereto other than the Company, enforceable against each of them in accordance with their respective terms and (iv) that the status of each of the Documents as legally valid and binding obligations of the parties will not be affected by any (a) breaches of, or defaults under, agreements or instruments, (b) violations of statutes, rules, regulations or court or governmental orders or (c) failures to obtain required consents, approvals or authorizations from, or to make required registrations, declarations or filings with, governmental authorities.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement and to the reference to our firm contained in the Prospectus under the heading “Legal Matters.” In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Latham & Watkins LLP