Exhibit 5.1

April 28, 2026

Capstone Green Energy Holdings, Inc.

16640 Stagg Street

Van Nuys, California 91406

Ladies and Gentlemen:

We have acted as counsel to Capstone Green Energy Holdings, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-3 (the “Registration Statement”), with the Securities and Exchange Commission (the “Commission”) covering the registration of up to 38,336,070 shares of common stock, par value $0.001 per share (the “Common Stock”) of the Company by the selling stockholders identified therein (the “Selling Stockholders” and each, a “Selling Stockholder”), consisting of (a) 3,593,847 shares of Common Stock (the “Initial 2025 PIPE Shares”) issued pursuant to a securities purchase agreement the Company entered into with certain Selling Stockholders on November 24, 2025 (the “2025 PIPE Purchase Agreement”); (b) up to 3,520,000 shares of Common Stock (the “2025 Warrant Shares”) issuable upon the exercise of pre-funded warrants (the “2025 Pre-Funded Warrants”) issued pursuant to the 2025 PIPE Purchase Agreement; (c) 3,588,889 shares of Common Stock (the “Initial 2026 PIPE Shares”) issued pursuant to a securities purchase agreement the Company entered into with certain Selling Stockholders on March 29, 2026 (the “2026 PIPE Purchase Agreement”); (d) up to 300,000 shares of Common Stock (the “2026 Warrant Shares” and together with the 2025 Warrant Shares, the “Warrant Shares”) issuable upon the exercise of pre-funded warrants (the “2026 Pre-Funded Warrants” and together with the 2025 Pre-Funded Warrants, the “Pre-Funded Warrants”) issued pursuant to the 2026 PIPE Purchase Agreement; (e) 3,333,334 shares of Common Stock (the “Preferred Investor Common Shares” and together with the Initial 2025 PIPE Shares and Initial 2026 PIPE Shares, the “Initial Common Shares”) issued pursuant to a securities purchase agreement, dated March 29, 2026, by and between the Company and certain Selling Stockholders (the “Preferred Investor Purchase Agreement” and together with the 2025 PIPE Purchase Agreement and the 2026 PIPE Purchase Agreement, the “Purchase Agreements”); and (f) 24,000,000 shares of Common Stock (the “Series A Conversion Shares” and together with the Initial Common Shares and Warrant Shares, the “Shares”) issuable upon the conversion of 80,000 shares (the “Preferred Shares” and together with the Preferred Investor Common Shares, the “Preferred Investor Shares”) of our newly designated Series A Convertible Preferred Stock, with a par value of $0.001 per share (the “Preferred Stock”), issued pursuant to the Preferred Investor Purchase Agreement.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Act”).

KATTEN MUCHIN ROSENMAN LLP

CHARLOTTE       CHICAGO       DALLAS       LOS ANGELES       NEW YORK
ORANGE COUNTY       SHANGHAI       WASHINGTON, DC

A limited liability partnership including professional corporations

LONDON: KATTEN MUCHIN ROSENMAN UK LLP

April 28, 2026

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In connection with this opinion, we have relied as to matters of fact, without investigation, upon affidavits, certificates and written statements of directors, officers and employees of, and the accountants for, the Company and on the accuracy of the representations of the Selling Stockholders. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such instruments, documents and records as we have deemed relevant and necessary to examine for the purpose of this opinion, including (i) the Registration Statement; (ii) the Purchase Agreements; (iii) the Pre-Funded Warrants; (iv) the Second Amended and Restated Certificate of Incorporation of the Company, as in effect on the date of the 2025 PIPE Purchase Agreement, the date of the issuance of the Initial 2025 PIPE Shares and the 2025 Pre-Funded Warrants and the date of this opinion, as certified by the Secretary of State of the State of Delaware on December 22, 2025 and an officer of the Company on December 22, 2025; (v) the Certificate of Designation of Series A Convertible Preferred Stock of Capstone Green Energy Holdings, Inc. (the “Certificate of Designation”), which was filed with the Secretary of State of the State of Delaware and became effective on March 31, 2026; (vi) the Second Amended and Restated Certificate of Incorporation of the Company, as amended, as in effect on the date of each of the 2026 PIPE Purchase Agreement and Preferred Investor Purchase Agreement, the date of the issuance of the Initial 2026 PIPE Shares, the Preferred Investor Shares and the 2026 Pre-Funded Warrants and the date of this opinion, as certified by the Secretary of State of the State of Delaware on April 24, 2026 and an officer of the Company on the date hereof; (vii) the Amended and Restated Bylaws of the Company, as in effect on the date of each of the Purchase Agreements, the dates of the issuance of the Initial Common Shares, the Preferred Shares and the Pre-Funded Warrants and the date of this opinion, as certified by an officer of the Company on the date hereof; (viii) records of proceedings and actions of the Board of Directors of the Company and the pricing committee of the Board of Directors, as applicable, relating to the issuance and sale of the Shares, the Preferred Shares and the Pre-Funded Warrants and related matters, as certified by an officer of the Company as of the date hereof; and (ix) such other instruments, documents, statements and records of the Company and others as we have deemed relevant and necessary to examine and rely upon for the purpose of this opinion.

In connection with this opinion, we have assumed the legal capacity of all natural persons, the accuracy and completeness of all documents and records that we have reviewed, the genuineness of all signatures, the due authority of the parties signing such documents, the authenticity of the documents submitted to us as originals and the conformity to authentic original documents of all documents submitted to us as copies. In making our examination of documents executed or to be executed by parties other than the Company, we have assumed that such parties had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and execution and delivery by such parties of such documents and the validity and binding effect thereof.

Based upon and subject to the foregoing, it is our opinion that:

Our opinions in respect of the Warrant Shares and Series A Conversion Shares expressed above are subject to the qualification that we express no opinion to the extent that, notwithstanding the Company’s current reservation of shares of Common Stock, future issuances of securities of the Company and/or antidilution adjustments to outstanding securities of the Company, may cause the Pre-Funded Warrants and/or Preferred Shares to be exercisable or convertible, as applicable, for more shares of Common Stock than the number that then remain authorized but unissued.

April 28, 2026

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This opinion is limited to the Delaware General Corporation Law, and we do not express any opinion concerning any other laws. This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion speaks only as of the date hereof, and we assume no obligation to revise or supplement this opinion after the date of effectiveness should the present laws of the State of Delaware be changed by legislative action, judicial decision or otherwise after the date hereof.

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

Very truly yours,

/s/ KATTEN MUCHIN ROSENMAN LLP

KATTEN MUCHIN ROSENMAN LLP