Dominion Energy Gas S-3 Shelf registration

Exhibit 5.1

December 15, 2023

Eastern Energy Gas Holdings, LLC

10700 Energy Way

Glen Allen, Virginia 23060

Re: Eastern Energy Gas Holdings, LLC

Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Eastern Energy Gas Holdings, LLC, a Virginia limited liability company (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration under the Securities Act and the proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act of the Company’s senior debt securities (the “Securities”). The Securities are to be issued under the indenture (the “Base Indenture”), dated as of October 1, 2013, by and between the Company (formerly known as Dominion Energy Gas Holdings, LLC) and Deutsche Bank Trust Company Americas, as trustee (the “Trustee”).

In arriving at the opinion expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the Base Indenture, a form of the Securities and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render this opinion. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. As to any facts material to this opinion, we have relied to the extent we deemed appropriate and without independent investigation upon statements and representations of officers and other representatives of the Company and others.

We have assumed without independent investigation that:

(i) at the time any Securities are sold pursuant to the Registration Statement (the “Relevant Time”), the Registration Statement and any supplements and amendments thereto (including post-effective amendments) will be effective and will comply with all applicable laws;

(ii) at the Relevant Time, a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby and all related documentation and will comply with all applicable laws;

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Eastern Energy Gas Holdings, LLC

December 15, 2023

Page 2

(iii) all Securities will be issued and sold in the manner stated in the Registration Statement and the applicable prospectus supplement;

(iv) at the Relevant Time, all corporate or other action required to be taken by the Company to duly authorize each proposed issuance of Securities and any related documentation (including the execution (in the case of certificated Securities), delivery and performance of the Securities and any related documentation referred to in our opinion below) shall have been duly completed and shall remain in full force and effect;

(v) at the Relevant Time, the Base Indenture shall have been duly qualified under the Trust Indenture Act of 1939, as amended;

(vi) the Base Indenture has been duly authorized by all necessary limited liability company action of the Company and duly executed and delivered by the Company and the other parties thereto; and

(vii) at the Relevant Time, a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Securities offered or issued will have been duly authorized by all necessary limited liability company action of the Company and duly executed and delivered by the Company and the other parties thereto.

Based on the foregoing and in reliance thereon, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that when:

a. the terms and conditions of any Securities have been duly established by supplemental indenture or officers’ certificate in accordance the terms and conditions of the Base Indenture,

b. any such supplemental indenture or officers’ certificate has been duly executed and delivered by the Company and the Trustee (together with the Base Indenture, the “Indenture”), and

c. such Securities have been executed (in the case of certificated Securities), delivered and authenticated in accordance with the terms of the Indenture and issued and sold for the consideration set forth in the applicable definitive purchase, underwriting or similar agreement,

such Securities will be legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

Eastern Energy Gas Holdings, LLC

December 15, 2023

Page 3

The opinion expressed above is subject to the following exceptions, qualifications, limitations and assumptions:

A. We render no opinion herein as to matters involving the laws of any jurisdiction other than the State of New York and the United States of America. This opinion is limited to the effect of the current state of the laws of the State of New York, the United States of America and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

B. The opinion above is subject to (i) the effect of any bankruptcy, insolvency, reorganization, moratorium, arrangement or similar laws affecting the rights and remedies of creditors generally, including without limitation the effect of statutory or other laws regarding fraudulent transfers or preferential transfers and (ii) general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies regardless of whether enforceability is considered in a proceeding in equity or at law.

C. We express no opinion regarding the effectiveness of (i) any waiver of stay, extension or usury laws; (ii) provisions relating to indemnification, exculpation or contribution, to the extent such provisions may be held unenforceable as contrary to public policy or federal or state securities laws or due to the negligence or willful misconduct of the indemnified party; (iii) any provision in the Indenture or Securities waiving the right to object to venue in any court; (iv) any agreement to submit to the jurisdiction of any Federal court; (v) any waiver of the right to jury trial or (vi) any provision to the effect that every right or remedy is cumulative and may be exercised in addition to any other right or remedy or that the election of some particular remedy does not preclude recourse to one or more others.

You have informed us that you intend to issue Securities from time to time on a delayed or continuous basis, and we understand that prior to issuing any Securities pursuant to the Registration Statement (i) you will advise us in writing of the terms thereof, and (ii) you will afford us an opportunity to (x) review the operative documents pursuant to which such Securities are to be issued or sold (including the applicable offering documents), and (y) file such supplement or amendment to this opinion (if any) as we may reasonably consider necessary or appropriate.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP