Exhibit 5.1

DLA Piper LLP (US)

1251 Avenue of the Americas

New York, New York 10020

www.dlapiper.com

T 212.335.4500

F 212.335.4501

April 2, 2020

Ross Stores, Inc.

5130 Hacienda Drive

Dublin, California 94568

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We serve as counsel to Ross Stores, Inc., a Delaware corporation (the “Company”), and have been requested to render this opinion in connection with the Registration Statement on Form S-3 of the Company (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) on April 2, 2020, including the prospectus included therein at the time the Registration Statement becomes effective (the “Prospectus”), under the Securities Act of 1933, as amended (the “Securities Act”), for registration by the Company of an unlimited amount of debt securities (the “Debt Securities”) issued in one or more series under a senior indenture dated September 18, 2014 (the “Indenture”), entered into by and between the Company and U.S. Bank National Association, pursuant to a resolution duly adopted by the Company’s Board of Directors (the “Board”) or a duly authorized committee thereof. The Registration Statement provides that the Debt Securities may be offered separately or together, in separate series, in amounts, at prices and on terms to be set forth in one or more supplements to the Prospectus (each, a “Prospectus Supplement”) or any related free writing prospectus (each, a “Free Writing Prospectus”).

In rendering the opinion expressed herein, we have reviewed originals or copies, certified or otherwise identified to our satisfaction, of the following documents (collectively, the “Documents”):

(a)The Registration Statement;

(b)The Corrected First Restated Certificate of Incorporation of Ross Stores, Inc., as amended by the Amendment of Certificate of Incorporation dated March 8, 2017, as in effect as of the date hereof (the “Charter”);

(c)The Amended and Restated By-Laws of Ross Stores, Inc., as in effect on the date hereof (the “Bylaws”);

(d)The Indenture;

(e)Resolutions adopted by the Board relating to the authorization of the filing of the Registration Statement and to the issuance of the Debt Securities, adopted by the Board of Directors of the Company;

(f)A certificate executed by the Secretary of the Company (the “Certificate”), dated as of the date hereof, as to certain factual matters; and

(g)Originals, or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates and other instruments as we have deemed necessary or appropriate for the purpose of rendering this opinion.

In examining the Documents, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the aforesaid documents, the completeness and authenticity of all documents submitted to us as originals, and the completeness and conformity with originals of all documents submitted to us as copies (and the completeness and authenticity of the originals of such copies), the absence of other agreements or understandings among the parties that would modify the terms of the proposed transactions or the respective rights or obligations of the parties thereunder and the accuracy and completeness of all public records reviewed by us. In making our examination of documents executed by parties other than the Company, we have assumed that such parties had the power and authority (corporate, trust, partnership or other) to enter into and perform all obligations thereunder, and we have also assumed the due authorization by all requisite action (corporate, trust, partnership or other) and the valid execution and delivery by such parties of such documents and the validity, binding effect and enforceability thereof with respect to such parties. As to all factual matters relevant to the opinions set forth below, we have relied, without independent verification, on certificates of officers of the Company, which we assume to be truthful, accurate and complete, and on the oral and written statements and representations of officers of the Company, of public officials and others.

We further assume that:

(a)The issuance, sale, amount and terms of the Debt Securities to be offered from time to time by the Company will be authorized and determined by proper action of the Board (or where permitted, a committee of the Board or designated officers) of the Company (each, a “Board Action”) in accordance with the Charter, Bylaws and applicable law, in each case so as not to result in a default under or breach of any instrument, document or agreement binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental or regulatory body having jurisdiction over the Company.

(b)The Company will not issue any Debt Securities in excess of the amount authorized by a Board Action.

(c)Any Debt Securities will be issued under the Indenture, accompanied by an officer’s certificate, that conforms to the description thereof set forth in the Prospectus, the applicable Prospectus Supplement and any related Free Writing Prospectus.

(d)To the extent that the obligations of the Company under the Indenture may be dependent upon such matters, the financial institution to be identified in such Indenture as trustee or in any other specified capacity (the “Financial Institution”) will be duly organized, validly existing, and in good standing under the laws of its jurisdiction of organization; the Financial Institution will be duly qualified to engage in the activities contemplated by such agreement; such agreement will have been duly authorized, executed, and delivered by the Financial Institution and will constitute the legally, valid and binding obligation of the Financial Institution enforceable against the Financial Institution in accordance with its terms; the Financial Institution will be in compliance, generally, with respect to acting under such agreement, with applicable laws and regulations; and the Financial Institution will have the requisite organizational and legal power and authority to perform its obligations under such agreement.

(e)Appropriate debentures, notes, bonds and/or other evidences of indebtedness evidencing the Debt Securities will be executed and authenticated in accordance with the Indenture, and

accompanied by an officer’s certificate, will be delivered upon the issuance and sale of the Debt Securities and will comply with the Indenture and any accompanying officer’s certificate, the Charter and Bylaws and applicable law.

(f)The underwriting or other agreements for offerings of the Debt Securities (each, an “Underwriting Agreement”) will be valid and legally binding contracts that conform to the description thereof set forth in the Prospectus, the applicable Prospectus Supplement and any related Free Writing Prospectus.

(g)At the time of the offer, sale and issuance of any Debt Securities, the Registration Statement will remain effective under the Securities Act.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications stated herein, it is our opinion that upon issuance and delivery of certificates for such Debt Securities against payment therefor in accordance with the terms and provisions of the applicable Board Action, the Debt Securities and the Indenture, any supplemental indenture (and/or an officer’s certificate, if any), the Registration Statement, the Prospectus, the applicable Prospectus Supplement and any related Free Writing Prospectus, and, if applicable, an Underwriting Agreement, the Debt Securities represented by such certificates will be duly authorized and validly issued, and, when duly authenticated in accordance with the terms of the Indenture and any supplemental indenture, will be valid and legally binding obligations of the Company.

In addition to the qualifications set forth above, the foregoing opinion is further qualified as follows:

(a)The foregoing opinion is rendered as of the date hereof. We assume no obligation to update such opinion to reflect any facts or circumstances that may hereafter come to our attention or changes in the law which may hereafter occur.

(b)We do not express any opinion herein concerning any law other than the Delaware General Corporation Law and the law of the State of New York (including the statutory provisions, all applicable provisions of the Constitution of Delaware and the New York Constitution and the reported judicial decisions interpreting the foregoing). The opinion expressed herein is subject to the effect of judicial decisions which may permit the introduction of parol evidence to modify the terms or the interpretation of agreements.

(c)We express no opinion as to compliance with the securities (or “blue sky”) laws of any jurisdiction.

(d)The opinion stated herein relating to the validity and binding nature of obligations of the Company is subject to (i) the effect of any applicable bankruptcy, insolvency (including, without limitation, all laws relating to fraudulent transfers), reorganization, moratorium or similar laws affecting creditors’ rights generally and (ii) the effect of general principles of equity (regardless of whether considered in a proceeding in equity or at law).

(e)This opinion is limited to the matters set forth herein, and no other opinion should be inferred beyond the matters expressly stated.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement and to the reference to our firm under the heading “Legal Matters” in the Registration Statement. In giving our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ DLA Piper LLP (US)

DLA PIPER LLP (US)