Exhibit 5.1​

Mayer Brown LLP
71 South Wacker Drive
Chicago, Illinois 60606-4637​

T: +1 312 782 0600
F: +1 312 701 7711
mayerbrown.com​

April 27, 2023

W.W. Grainger, Inc.
100 Grainger Parkway
Lake Forest, IL 60045

Re:

W.W. Grainger, Inc. Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to W.W. Grainger, Inc., an Illinois corporation (the “Company”), in connection with the proposed issuance from time to time, pursuant to Rule 415 under the Securities Act of 1933, as amended (the “Securities Act”), of the Company’s debt securities (the “Debt Securities”) as set forth in the Registration Statement on Form S-3 of the Company filed with the Securities and Exchange Commission (the “SEC”) on the date hereof (the “Registration Statement”). Each series of Debt Securities will be issued under an indenture, dated as of June 11, 2015 (as amended and supplemented, the “Indenture”), between the Company and U.S. Bank Trust Company, National Association, as successor in interest to U.S. Bank National Association, as trustee. Certain terms of the Debt Securities will be approved by the Board of Directors of the Company or a committee thereof as part of the corporate action to be taken in connection with the authorization of the issuance of the Debt Securities (the “Corporate Proceedings”).

As counsel to the Company, we have examined originals or copies certified or otherwise identified to our satisfaction of resolutions of the Board of Directors of the Company and such records, certificates and other documents of the Company and such questions of law as we considered necessary or appropriate for the purpose of this opinion. As to certain facts material to our opinion, we have relied, to the extent we deem such reliance proper, upon certificates of public officials and officers of the Company. In rendering this opinion, we have assumed the legal capacity and genuineness of all signatures of persons signing all documents, the authenticity, accuracy and completeness of all documents, records and certificates submitted to us as originals and the conformity to authentic original documents, records and certificates of all documents, records and certificates submitted to us as copies. As to all parties other than the Company, we have assumed the due authorization, execution and delivery of all documents, and we have assumed the validity and enforceability of all documents against all parties thereto, other than the Company, in accordance with their respective terms.

Based upon and subject to the foregoing and to the assumptions, conditions and limitations set forth herein, we are of the opinion that, upon the completion of the Corporate Proceedings relating to a series of Debt Securities and the due execution, authentication, issuance and delivery of the Debt Securities of such series, the Debt Securities of such series, when sold in exchange for the consideration set forth in the prospectus contained in the Registration Statement (the “Prospectus”) and any prospectus supplement relating to such series of Debt Securities, will be duly authorized and will be binding obligations of the Company, enforceable in accordance with their terms and entitled to the benefits of the Indenture, except as such enforceability may be limited by bankruptcy, insolvency, reorganization or similar laws affecting creditors’ rights generally or public policy considerations and subject to general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law).

Mayer Brown is a global services provider comprising an association of legal practices that are separate entities including
Mayer Brown LLP (Illinois, USA), Mayer Brown International LLP (England), Mayer Brown (a Hong Kong partnership)
and Tauil & Chequer Advogados (a Brazilian partnership).

Mayer Brown LLP

W.W. Grainger, Inc.
April 27, 2023
Page 2

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to being named in the Prospectus and any related prospectus supplement under the caption “Legal Matters” with respect to the matters stated therein. In giving this consent, we do not thereby admit that we are experts within the meaning of Section 11 of the Securities Act or within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC.

We are admitted to practice law in the State of Illinois, and we express no opinion as to matters under or involving any laws other than the laws of the State of Illinois, the laws of the State of New York and the federal laws of the United States of America.

This opinion is expressly limited to the matters set forth above and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company or any other person, or any other document or agreement involved with issues addressed herein. We assume no obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinions expressed herein.

This opinion is furnished in connection with the filing of the Registration Statement and is not to be used, circulated, quoted or otherwise relied upon for any other purpose.

Sincerely,

/s/ Mayer Brown LLP

Mayer Brown LLP