Exhibit 5.1

Chicago New York Washington, DC London San Francisco Los Angeles Singapore vedderprice.com

January 11, 2021

Ladies and Gentlemen:

We have acted as counsel to GraniteShares LLC, a Delaware limited liability company (the “Sponsor”), in its capacity as the sponsor of GraniteShares Platinum Trust, a business trust formed under the laws of the State of New York (the “Trust”), in connection with the Trust’s filing on January 11, 2021 with the Securities and Exchange Commission (the “Commission”) of its Registration Statement on Form S-1 (the “Registration Statement”), including the prospectus in Part I of the Registration Statement (the “Prospectus”), under the Securities Act of 1933, as amended (the “1933 Act”), relating to the issuance and sale by the Trust of 7,150,000 units of fractional undivided beneficial interest in the net assets of the Trust (the “Shares”).

You have requested our opinion as to the matters set forth below in connection with the filing of the Registration Statement. In connection with rendering this opinion, we have examined: (a) the Registration Statement, (b) the Depositary Trust Agreement between the Sponsor and The Bank of New York Mellon, as trustee (the “Trustee”), dated as of January 11, 2018 (the “Depository Trust Agreement”), (c) the Allocated Platinum Account Agreement between the Trustee and ICBC Standard Bank PLC, as custodian (the “Custodian”), dated as of January 11, 2018, (d) the Unallocated Platinum Account Agreement between the Trustee and the Custodian, dated as of January 11, 2018, and (e) such other instruments, documents and records of the Trust and others as we, in our professional judgment, have deemed necessary or appropriate as a basis for the opinion set forth below.

In connection with this opinion, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents and records that we have reviewed, the authenticity of the documents purporting to be originals and the conformity to originals of all documents submitted to us as copies. We have further assumed the Trust has been validly formed and is validly existing, that neither the Trust nor the Trustee has taken any action to terminate the Trust and that the Trustee has the power and authority to perform its obligations under the Depository Trust Agreement. As to questions of fact material to our opinion, we have relied (without investigation or independent confirmation) upon the representations contained in the above-described documents and on certificates and other communications from public officials, and officers and the Trustee of the Trust. Our opinion, as set forth herein, is based on facts in existence on the date hereof, and is limited to the laws of the State of New York that are applicable to the issuance of units of fractional undivided beneficial interest in the net assets of business trusts. We express no opinion with respect to any other laws or regulations. Without limiting the generality of the foregoing, we express no opinion as to any state securities or broker-dealer laws or regulations thereunder relating to the offer, issuance and sale of the Shares.

1633 Broadway, 31st Floor | New York, New York 10019 | T +1 212 407 7700 | F +1 212 407 7799

Vedder Price P.C. is affiliated with Vedder Price LLP, which operates in England and Wales, Vedder Price (CA), LLP, which operates in California, and Vedder Price Pte. Ltd., which operates in Singapore.

GraniteShares LLC

as Sponsor to GraniteShares Platinum Trust

January 11, 2021

Page 2

Based upon and subject to the foregoing and the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Shares proposed to be offered and sold pursuant to the Registration Statement, when it is made effective by the Commission or otherwise pursuant to the rules and regulations of the Commission, and when such Shares are issued in accordance with the terms of the Depository Trust Agreement, including receipt by the Trustee of the consideration required for the issuance of Shares, will have been validly authorized by the Trust and, when sold in accordance with the terms of and in the manner contemplated by the Registration Statement, will be validly issued, fully paid and non-assessable.

This opinion is rendered in connection with the filing of the Registration Statement. We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement and to the use of our name in the Prospectus under the caption “Legal Matters,” and in any revised or amended versions thereof. 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 1933 Act or the rules and regulations of the Commission thereunder. Except as specifically authorized above in this paragraph, this opinion is not to be quoted in whole or in part or otherwise referred to, nor is it to be filed with any government agency or any other person, without, in each case, our prior written consent. This opinion is given to you as of the date hereof, and we assume no obligation to advise you of any change that may hereafter be brought to our attention. The opinions expressed herein are matters of professional judgment and are not a guarantee of result.