Exhibit 5.1

March 26, 2018

Pure Storage, Inc.

650 Castro Street, Suite 400

Mountain View, California 94041

Re: Pure Storage, Inc. - Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to Pure Storage, Inc., a Delaware corporation (the “Company”), in connection with the filing of a registration statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission covering the offering of up to 13,258,737 shares of the Company’s Class A Common Stock (the “Common Stock”), par value $0.0001 per share, consisting of (i) 11,048,948 shares of Common Stock (the “2015 EIP Shares”) issuable pursuant to the Company’s 2015 Equity Incentive Plan and (ii) 2,209,789 shares of Common Stock (the “2015 ESPP Shares” and, together with the 2015 EIP Shares, the “Shares”) issuable pursuant to the Company’s 2015 Employee Stock Purchase Plan (together with the Company’s 2015 Equity Incentive Plan, the “Plans”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and related prospectuses, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, (c) the Plans and (d) originals or copies certified to our satisfaction of such other records, documents, certificates, memoranda and other instruments as we deem 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 thereof. 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 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, we are of the opinion that the Shares, when sold and issued in accordance with the Plans, the Registration Statement and related prospectuses, will be validly issued, fully paid, and nonassessable (except as to shares issued pursuant to certain deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

Cooley LLP

By: /s/ Seth J. Gottlieb                

Seth J. Gottlieb