Exhibit 99.5
1.1 - Florian Schönharting 1.4 - Duncan Moore, PhD 1.2 - Michael Forer,
LL.B. 1.3 - Dermot Hanley 4 3 B M For Against Abstain For Against Abstain For Against Abstain The Sample Company Proposals — The Board of Directors recommends a vote FOR all the nominees listed and FOR Proposals 2, 3 and
4. A 045XWC 2. To ratify the appointment of PricewaterhouseCoopers Ireland as independent auditors of the Company for the year ending 31 December 2025 and to authorise the Board to fix the remuneration of the auditors. 4. To renew the
Board’s existing authority under Irish law to allot and issue ordinary shares for cash without first offering those shares to existing shareholders pursuant to the statutory pre-emption right that would otherwise apply. 3. To renew the
Board’s existing authority under Irish law to allot and issue ordinary shares. 1. Election of Directors: For Against Abstain For Against Abstain Please sign exactly as your name(s) appear(s) hereon. When signing as attorney, executor,
administrator, or other fiduciary please give full title as such. Joint owners should each sign personally. All holders must sign. If a corporation or partnership, please sign in full corporate or partnership name by authorized
officer Date (mm/dd/yyyy) — Please print date below. Signature 1 — Please keep signature within the box. Signature 2 — Please keep signature within the box. Authorized Signatures — This section must be completed for your vote to count.
Please date and sign below. B 2025 GH Research PLC Annual General Meeting Proxy Card 1234 5678 9012 345 Using a black ink pen, mark your votes with an X as shown in this example. Please do not write outside the designated areas. T IF
VOTING BY MAIL, SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE.T In their discretion, the proxies are authorized to vote upon any other business that may properly come before the meeting or any adjournment(s) or
postponement(s) thereof. MMMMMMMMMMMM MMMMMMMMM 6 5 6 6 0 6 If no electronic voting, delete QR code and control # 000001 MR A SAMPLE DESIGNATION (IF ANY) ADD 1 ADD 2 ADD 3 ADD 4 ADD 5 ADD 6 ENDORSEMENT_LINE SACKPACK
000000000.000000 ext 000000000.000000 ext 000000000.000000 ext C123456789 000000000.000000 ext 000000000.000000 ext 000000000.000000 ext MR A SAMPLE (THIS AREA IS SET UP TO ACCOMMODATE 140 CHARACTERS) MR A SAMPLE AND MR A SAMPLE
AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND C 1234567890 J N T MMMMMMM Your vote matters – here’s how to vote! You may vote online or by phone instead of mailing this card. Votes
submitted electronically must be received by 11:59 P.M., Irish Standard Time on 30 July 2025. Online Go to www.envisionreports.com/ghrs or scan the QR code — login details are located in the shaded bar below. Phone Call toll free
1-800-652-VOTE (8683) within the USA, US territories and Canada or 1-781-575-2300 if outside these areas.
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electronic delivery, sign up at www.envisionreports.com/ghrs GH Research PLC Annual General Meeting of Shareholders on July 31, 2025 at 2:00 p.m. Irish Standard Time This proxy is solicited by the Board of Directors The shareholder(s)
hereby appoint(s) Magnus Halle and Julie Ryan, or either of them, as proxies, each with the power to appoint his/her substitute, and hereby authorises them to represent and to vote, as designated on the reverse side of this ballot, all of
the ordinary shares of GH Research PLC that the undersigned shareholder(s) is/are entitled to vote, with all powers which the undersigned would possess if personally present at the meeting, at the Annual General Meeting of Shareholders to
be held on July 31, 2025 at 2:00 P.M., Irish Standard Time at Joshua Dawson House, Dawson Street, Dublin 2, D02 RY95, Ireland and at any adjournment or postponement thereof. You may vote at the Annual General Meeting if you were a
shareholder of record at the close of business on 6 June 2025. A shareholder entitled to attend and vote is entitled to appoint one or more proxies to attend, speak and vote instead of him or her at the Annual General Meeting. A proxy need
not be a shareholder of record. If you wish to nominate a proxy other than Magnus Halle or Julie Ryan, please contact our Company Secretary at Joshua Dawson House, Dawson Street, Dublin 2, D02 RY95, Ireland. Any such nominated proxy must
attend the Annual General Meeting in person in order for your votes to be cast. This proxy, when properly executed, will be voted in the manner directed herein. If no such direction is made, this proxy will be voted in accordance with the
Board of Directors’ recommendations. In his/her discretion, the proxies are authorised to vote upon such other business as may properly come before the meeting, and any adjournment or postponement thereof. Non-Voting Items C T IF VOTING
BY MAIL, SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE.T Change of Address — Please print new address below. Comments — Please print your comments below. Important notice regarding the Internet availability of proxy
materials for the Annual General Meeting of Shareholders. The Notice of Annual General Meeting, Irish Statutory Financial Statements and Form 20-F are available at: www.envisionreports.com/ghrs 2025 Annual General Meeting Admission
Ticket 2025 Annual General Meeting of Shareholders of GH Research PLC July 31, 2025 at 2:00 P.M., Irish Standard Time Joshua Dawson House, Dawson Street, Dublin 2, D02 RY95, Ireland Upon arrival, please present this admission ticket and
photo identification at the registration desk.