nrgveloc-lwexhibit51opin

300 Colorado Street, Suite 2400 Austin, TX 78701 Tel: +1.737.910.7300 Fax: +1.737.910.7301 www.lw.com FIRM / AFFILIATE OFFICES Austin Milan Beijing Munich Boston New York Brussels Orange County Century City Paris Chicago Riyadh Dubai San Diego Düsseldorf San Francisco Frankfurt Seoul Hamburg Silicon Valley Hong Kong Singapore Houston Tel Aviv London Tokyo Los Angeles Washington, D.C. Madrid June 4, 2025 4165 East Thousand Oaks Blvd. Suite 100 Westlake Village, CA 91362 Re: Registration No. 333-273089 To the addressees set forth above: We have acted as special counsel to Energy Vault Holdings, Inc., a Delaware corporation (the “Company”), in connection with that certain Equity Purchase Agreement, dated as of March 31, 2025 (as amended, supplemented or otherwise modified, the “Purchase Agreement”), by and between the Company and Hudson Global Ventures, LLC (the “Investor”), including the issuance of (i) 452,000 shares (the “Commitment Shares”) of Common Stock, par value $0.0001 per share, of the Company (the “Common Stock”) that were issued to the Investor by the Company as consideration for the Investor’s commitment to purchase shares of Common Stock pursuant to the Purchase Agreement and (ii) up to $25,000,000 worth of shares of Common Stock (the “Put Shares” and, together with the Commitment Shares, the “Shares”) that may be issued and sold to the Investor from time to time by the Company in connection with the Purchase Agreement pursuant to (i) a registration statement on Form S-3 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on June 30, 2023 (Registration No. 333-273089) (as so filed and as amended, the “Registration Statement”), (ii) a base prospectus, dated June 30, 2023, included in the Registration Statement (the “Base Prospectus”), and (iii) a prospectus supplement, dated May 30, 2025, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or the Prospectus, other than as expressly stated herein with respect to the issuance of the Shares. As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws. Exhibit 5.1

June 4, 2025 Page 2 Subject to the foregoing and the other matters set forth herein, it is our opinion that, upon the completion of all Corporate Proceedings (as defined below) relating to any Shares, when such Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers and have been issued by the Company against payment therefor (not less than par value) in accordance with the Corporate Proceedings and in the circumstances contemplated by the Purchase Agreement, the issuance and sale of such Shares by the Company will have been duly authorized by all necessary corporate action of the Company, and such Shares will be validly issued, fully paid and nonassessable. In rendering the foregoing opinion, we have assumed that (i) the Company complied or will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL, (ii) upon the issuance of any of the Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its certificate of incorporation and (iii) certain terms of the Shares to be issued by the Company from time to time will be authorized and approved by the board of directors of the Company (the “Board”) and/or one or more committees thereof established by the Board with the authority to issue and sell Shares pursuant to the Purchase Agreement in accordance with the DGCL, the Company’s certificate of incorporation, the Company’s bylaws and certain resolutions of the Board and/or one or more committees thereof (with such approvals referred to herein as the “Corporate Proceedings”) prior to issuance thereof. This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Company’s Form 8-K dated June 4, 2025 and to the reference to our firm contained in the Prospectus under the heading “Legal Matters.” 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 Act or the rules and regulations of the Commission thereunder. Sincerely, /s/ Latham & Watkins LLP