Exhibit 5.1

Charles J. Bair

T: +1 858 550 6142

cbair@cooley.com

October 28, 2015

Kura Oncology, Inc.

11119 N. Torrey Pines Road, Suite 125

La Jolla, CA 92037

Ladies and Gentlemen:

You have requested our opinion, as counsel to Kura Oncology, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement (No. 333-207534) on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering an underwritten public offering of up to 4,312,500 shares (the “Shares”) of the Company’s common stock, par value $0.0001, including up to 562,500 Shares that may be sold pursuant to the exercise of an option to purchase additional shares. All of the Shares are to be sold by the Company as described in the Registration Statement and the Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement and Prospectus, the Company’s Amended and Restated Certificate of Incorporation, its Amended and Restated Bylaws and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.

We have assumed the genuineness and authenticity of all documents submitted to us as originals and the conformity to originals of all documents submitted to us as copies. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought independently to verify such matters. Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction are applicable to the subject matter hereof. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities, or to the sale or issuance thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and non-assessable.

4401 EASTGATE MALL, SAN DIEGO, CA 92121 T: (858) 550-6000 F: (858) 550-6420 WWW.COOLEY.COM

Kura Oncology, Inc.

October 28, 2015

Page Two

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement.

4401 EASTGATE MALL, SAN DIEGO, CA 92121 T: (858) 550-6000 F: (858) 550-6420 WWW.COOLEY.COM