Exhibit 5.1

Laura A. Berezin

+1 650 843 5128

lberezin@cooley.com

November 6, 2018

Five Prime Therapeutics, Inc.

Two Corporate Drive

South San Francisco, CA 94080

Ladies and Gentlemen:

We have acted as counsel to Five Prime Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the filing of a Registration Statement on Form S-3 (the “Registration Statement”) by the Company under the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement includes a prospectus (the “Base Prospectus”) that provides it will be supplemented in the future by one or more prospectus supplements (each, a “Prospectus Supplement”). The Registration Statement, including the Base Prospectus as supplemented from time to time by one or more Prospectus Supplements, will provide for the registration by the Company of the offer and sale of shares of common stock, par value $0.001 per share, of the Company (the “Common Stock”). The Common Stock is being registered for offer and sale from time to time pursuant to Rule 415 under the Securities Act.

In connection with this opinion, we have examined and relied upon originals, or copies certified to our satisfaction, of such records, documents, certificates, opinions, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

In rendering this opinion, we have assumed the genuineness and authenticity of all signatures on original documents; the authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents where authorization, execution and delivery are prerequisites to the effectiveness of such documents. We have assumed that, at the time of issuance and sale, a sufficient number of shares of Common Stock is authorized and available for issuance and that the consideration for the issuance and sale of the Common Stock is in an amount that is not less than the par value of the Common Stock.

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware. Our opinion is based on these laws as in effect on the date hereof. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing and in reliance thereon, and subject to the qualifications herein stated, we are of the opinion that, provided that (i) the Registration Statement and any required

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post-effective amendment thereto have become effective under the Securities Act and the Base Prospectus and any and all Prospectus Supplement(s) required by applicable laws have been delivered and filed as required by such laws; (ii) the issuance of the Common Stock has been duly authorized by all necessary corporate action on the part of the Company; (iii) the issuance and sale of the Common Stock do not violate any applicable law, are in conformity with the Company’s then operative certificate of incorporation and bylaws do not result in a default under or breach of any agreement or instrument binding upon the Company and comply with any applicable requirement or restriction imposed by any court or governmental body having jurisdiction over the Company; and (iv) the certificates, if any, for the Common Stock have been duly executed by the Company, countersigned by the transfer agent therefor and duly delivered to the purchasers thereof against payment therefor, then the Common Stock, when issued and sold as contemplated in the Registration Statement, the Base Prospectus and the related Prospectus Supplement(s), and in accordance with a duly authorized, executed and delivered purchase, underwriting or similar agreement, will be validly issued, fully paid and non-assessable.

[SIGNATURE PAGE FOLLOWS]

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We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Base Prospectus. We further consent to the incorporation by reference of this opinion into any registration statement or post-effective amendment thereto filed pursuant to Rule 462(b) under the Securities Act with respect to additional Securities, and any such additional Securities will also be covered by this opinion.

Our opinion set forth above is limited to the matters expressly set forth in this letter, and no opinion is implied or may be inferred beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof, and we undertake no obligation or responsibility to update or supplement this opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur. Sincerely,

Cooley LLP
By:	/s/ Laura A. Berezin
	LAURA A. BEREZIN

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