Exhibit 5.1

John T. McKenna

+1 650 843 5059

jmckenna@cooley.com

September 24, 2015

Pure Storage, Inc.

650 Castro Street, Suite 400

Mountain View, CA 94041

Ladies and Gentlemen:

We have acted as counsel to Pure Storage, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement (No. 333-206312) 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 28,750,000 shares of the Company’s Class A common stock, par value $0.0001 (the “Shares”), to be sold by the Company (including up to 3,750,000 Shares that may be sold by the Company upon exercise of an over-allotment option granted to the underwriters).

In connection with this opinion, we have (i) examined and relied upon (a) the Registration Statement and Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, as currently in effect as of the date hereof and (c) 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 and (ii) assumed that the Shares will be sold at a price established by the Board of Directors of the Company or the Pricing Committee thereof in accordance with Section 153 of the General Corporation Law of the State of Delaware (the “DGCL”).

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 and the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof (except we have not assumed the due execution and delivery by the Company of any such documents). As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought to independently verify such matters. Our opinion is expressed only with respect to the DGCL.

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

3175 HANOVER STREET, PALO ALTO, CA 94304-1130  T: (650) 843-5000  F: (650) 849-7400  WWW.COOLEY.COM

Pure Storage, Inc.

September 24, 2015

Page Two

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

3175 HANOVER STREET, PALO ALTO, CA 94304-1130  T: (650) 843-5000  F: (650) 849-7400  WWW.COOLEY.COM