Exhibit 5.1

Brownstein Hyatt Farber Schreck, LLP

702.382.2101 main

100 North City Parkway, Suite 1600

Las Vegas, Nevada 89106

September 9, 2025

Gemini Space Station, Inc.

600 Third Avenue, 2^nd Floor

New York, NY 10016

To the addressee set forth above:

We have acted as local Nevada counsel to Gemini Space Station, Inc., a Nevada corporation (the “Company”), in connection with the filing by the Company of Amendment No. 3 to the Registration Statement on Form S-1 (File No. 333-289665) (the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), including the preliminary prospectus contained therein (the “Prospectus”), relating to (i) the issuance and sale by the Company of up to 16,666,667 shares (the “Firm Shares”, and together with the Option Shares (as defined below), the “Shares”) of the Company’s Class A common stock, par value $0.001 per share (the “Class A Common Stock”), and (ii) pursuant to an overallotment option under the Underwriting Agreement (as defined below), the (a) issuance and sale by the Company of up to an additional 729,699 shares of Class A Common Stock (the “Company Option Shares”) and (b) sale by the Selling Stockholders (as defined in the Underwriting Agreement) of up to 103,634 shares of Class A Common Stock (the “Selling Stockholder Shares”, and together with the Company Option Shares, the “Option Shares”), all pursuant to an underwriting agreement by and between the Company and Goldman Sachs & Co. LLC and Citigroup Global Markets Inc., as representatives of the underwriters (the “Underwriting Agreement”). This opinion letter is being furnished at your request in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In our capacity as such counsel, we are familiar with the proceedings taken and proposed to be taken by the Company in connection with the registration of the Shares as described in the Registration Statement and the Prospectus. For purposes of this opinion letter, and except to the extent set forth in the numbered opinion paragraphs below, we have assumed that all such proceedings have been timely completed or will be timely completed in the manner presently proposed in the Registration Statement and the Prospectus.

For purposes of issuing this opinion letter, we have made such legal and factual examinations and inquiries, including an examination of originals or copies certified or otherwise identified to our satisfaction as being true copies of (i) the Registration Statement (including the Prospectus), (ii) the articles of incorporation and bylaws of the Company, each as amended to date, (iii) the forms of the amended and restated articles of incorporation and amended and restated bylaws of the Company filed as exhibits to the Registration Statement (collectively, the “A&R Governing Documents”), (iv) the form of the Underwriting Agreement filed as an exhibit to the Registration Statement, and (v) such agreements, instruments and other documents, or forms thereof, as we have deemed necessary or appropriate, and we have obtained from officers and other representatives and agents of the Company, and have relied upon, such certificates, representations and assurances as we have deemed necessary or appropriate.

www.bhfs.com

Gemini Space Station, Inc.

September 9, 2025

Page 2

Without limiting the generality of the foregoing, in our examination and in issuing this opinion letter, we have, with your permission, assumed without independent verification that (i) the Underwriting Agreement will be duly authorized, executed and delivered by each party thereto, in substantially the form thereof filed as an exhibit to the Registration Statement; (ii) the obligations of each party set forth in the Underwriting Agreement will be its valid and binding obligations, enforceable in accordance with their respective terms; (iii) (A) the Company has taken or will take all corporate action required in connection with the authorization, execution and delivery of the Underwriting Agreement, (B) each of the A&R Governing Documents, in the respective forms thereof that have been filed as exhibits to the Registration Statement, will be effective and in full force and effect prior to any issuance of Shares, and (C) all Shares will be offered, issued and sold in compliance with all applicable laws, the A&R Governing Documents and the Underwriting Agreement ((iii)(A) through (iii)(C), inclusive, above are referred to collectively herein as the “Corporate Proceedings”)); (iv) except to the extent set forth in the numbered opinion paragraphs below, the statements of fact and representations and warranties set forth in the documents we have reviewed, including the Underwriting Agreement, are or will at all relevant times be, true and correct as to factual matters; (v) each natural person executing a document, at the time of such execution, has or will have sufficient legal capacity to do so; (vi) all documents submitted to us as originals are authentic, the signatures on all documents that we have examined are genuine, and all documents submitted to us as certified, conformed, photostatic, electronic or facsimile copies conform to the original documents; and (vii) all corporate records made available to us by the Company and all public records we have reviewed are accurate and complete.

We are qualified to practice law in the State of Nevada. The opinions set forth herein are expressly limited to and based exclusively on the general corporate laws of the State of Nevada, and we do not purport to be experts on, or to express any opinion with respect to the applicability thereto or the effect thereon of, the laws of any other jurisdiction. We express no opinion concerning, and we assume no responsibility as to laws or judicial decisions related to, or any orders, consents or other authorizations or approvals as may be required by, any federal laws, rules or regulations, including, without limitation, any federal securities laws, rules or regulations, or any state securities or “blue sky” laws, rules or regulations.

Based on the foregoing, and in reliance thereon, and having regard to legal considerations and other information that we deem relevant, we are of the opinion that:

1. The Company is validly existing as a corporation and in good standing under the laws of the State of Nevada.

2. If and when all Corporate Proceedings have been taken and completed, including in respect of any offering, issuance or sale of Firm Shares, such Firm Shares will be duly authorized by the Company, and if, when and to the extent such Firm Shares are issued and sold in accordance with all applicable terms and conditions set forth in, and in the manner contemplated by, the Underwriting Agreement (including payment in full of any and all consideration required for such Firm Shares as prescribed thereunder), and in the manner described in the Registration Statement and the Prospectus, such Firm Shares will be validly issued, fully paid and nonassessable.

Gemini Space Station, Inc.

September 9, 2025

Page 3

3. If and when all Corporate Proceedings have been taken and completed, including in respect of any offering, issuance or sale of Company Option Shares, such Company Option Shares will be duly authorized by the Company, and if, when and to the extent such Company Option Shares are issued and sold in accordance with all applicable terms and conditions set forth in, and in the manner contemplated by, the Underwriting Agreement (including payment in full of any and all consideration required for such Company Option Shares as prescribed thereunder), and in the manner described in the Registration Statement and the Prospectus, such Company Option Shares will be validly issued, fully paid and nonassessable.

4. If and when all Corporate Proceedings have been taken and completed, including in respect of the issuance of the Selling Stockholder Shares, such Selling Stockholder Shares will be duly authorized, validly issued, fully paid and nonassessable.

The opinions expressed herein are based upon the applicable laws of the State of Nevada and the facts in existence on the date hereof. In delivering this opinion letter to you, we disclaim any obligation to update or supplement the opinions set forth herein or to apprise you of any changes in such laws or facts after such time as the Registration Statement is declared effective. No opinion is offered or implied as to any matter, and no inference may be drawn, beyond the strict scope of the specific issues expressly addressed by the opinions set forth herein.

We consent to your filing this opinion letter as an exhibit to the Registration Statement and to the reference to our firmin the Prospectus under the heading “Legal Matters”. In giving such consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Brownstein Hyatt Farber Schreck, LLP

Gemini Space Station, Inc. S-1/A