Exhibit 5.1

|  | 787 Seventh Avenue New York, NY 10019-6099 Tel: 212 728 8000 Fax: 212 728 8111

January 13, 2026

Ryerson Holding Corporation

227 W. Monroe St. 27th Floor

Chicago, Illinois 60606

Re: | Ryerson Holding Corporation- Issuance of Common Stock in Connection with the Acquisition of Olympic Steel, Inc.

Ladies and Gentlemen:

We have acted as counsel to Ryerson Holding Corporation, a corporation organized under the laws of the State of Delaware (the “Company”), and Crimson MS Corp., an Ohio corporation and a direct wholly owned subsidiary of the Company (“Merger Sub”), in connection with (i) the proposed transactions contemplated by the Agreement and Plan of Merger, dated as of October 28, 2025, by and among the Company, Merger Sub, and Olympic Steel, Inc., an Ohio corporation (as may be amended from time to time, the “Merger Agreement”), and (ii) the preparation of the Registration Statement on Form S-4 (Registration No. 333-291983) (as may be amended from time to time, the “Registration Statement”) initially filed by the Company on December 5, 2025 with the U.S. Securities and Exchange Commission (the “SEC”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), for the registration of shares of the Company’s common stock, par value $0.01 per share (the “Shares”), issuable in connection with the proposed transactions and in accordance with the terms and subject to the conditions set forth in the Merger Agreement.

In rendering this opinion, we have examined the Registration Statement, the Merger Agreement, copies of the Third Amended and Restated Certificate of Incorporation of the Company, the Second Amended and Restated Bylaws of the Company, resolutions adopted by the Company’s Board of Directors, and other records and documents that we have deemed necessary for the purpose of this opinion. We have also examined such other documents, papers, statutes and authorities as we have deemed necessary or advisable to form a basis for the opinion hereinafter expressed.

In our examination, we have assumed the genuineness of all signatures and the conformity to original documents of all copies submitted to us. As to various questions of fact material to our opinion, we have relied on statements and certificates of officers and representatives of the Company and public officials.

BRUSSELSCHICAGODALLASFRANKFURTHAMBURGHOUSTON LONDONLOS ANGELES

MILANMUNICHNEW YORKPALO ALTOPARISROMESAN FRANCISCOWASHINGTON

Ryerson Holding Corporation

January 13, 2026

Page 2

Based on the foregoing, and subject to the qualifications and limitations set forth below, we are of the opinion that the Shares, when duly issued in accordance with the terms of the prospectus included as part of the Registration Statement and in accordance with the terms and subject to the conditions set forth in the Merger Agreement, will be validly issued, fully paid and non-assessable.

This opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. We do not express an opinion as to matters arising under the laws of any jurisdiction, other than the laws of the State of New York and the General Corporation Law of the State of Delaware (and the applicable provisions of the Delaware Constitution and reported judicial decisions interpreting such law) and the federal laws of the United States of America.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us in the prospectus included as part of the Registration Statement. In giving such 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 or regulations of the SEC promulgated thereunder. We assume no obligation to advise you or any other person, or to make any investigations, as to any legal developments or factual matters arising subsequent to the date of effectiveness of the Registration Statement that might affect the opinions expressed herein.

Very truly yours,
/s/ Willkie Farr & Gallagher LLP