Exhibit 5.1

	601 Lexington Avenue New York, NY 10022 United States +1 212 446 4800 www.kirkland.com	Facsimile: +1 212 446 4900

March 26, 2021

ARYA Sciences Acquisition Corp III

51 Astor Place, 10th Floor

New York, New York 10003

Ladies and Gentlemen:

We have acted as special legal counsel to ARYA Sciences Acquisition Corp III, a Cayman Islands exempted company (“ARYA”), in connection with the Registration Statement on Form S-4, initially filed with the U.S. Securities and Exchange Commission (the “Commission”) on March 26, 2021 pursuant to the Securities Act of 1933, as amended (the “Act”) (such Registration Statement, as the same may be amended or supplemented, is hereafter referred to as the “Registration Statement”), relating to the Business Combination Agreement, dated February 7, 2021 (as may be amended, supplemented or otherwise modified from time to time, the “Business Combination Agreement”), by and among ARYA, Mako Merger Sub, Inc., a Delaware corporation (“Merger Sub”), and Nautilus Biotechnology, Inc., a Delaware corporation (“Nautilus”). Pursuant to the Business Combination Agreement, ARYA will change its jurisdiction of incorporation through the transfer by way of continuation and deregistration of ARYA from the Cayman Islands and the continuation and domestication of ARYA as a corporation incorporated in the State of Delaware (the “Domestication”).

In connection with the Domestication, ARYA will change its jurisdiction of incorporation from the Cayman Islands to Delaware pursuant to Part XII of the Companies Law (Revised) of the Cayman Islands and domesticate as a Delaware corporation in accordance with Section 388 of the General Corporation Law of the State of Delaware (the “DGCL”) by filing a certificate of corporate domestication simultaneously with a certificate of incorporation, in each case in respect of ARYA with the Secretary of State of the State of Delaware (the “Delaware Secretary of State”). The Domestication is subject to the approval of the shareholders of ARYA. We refer herein to ARYA following effectiveness of the Domestication as “New Nautilus”.

Promptly following the consummation of the Domestication, Merger Sub will merge with and into Nautilus (the “Merger” and together with the Domestication and related transactions, the “Business Combination”), with Nautilus as the surviving company in the Merger and, after giving effect to the Merger, Nautilus will be a wholly-owned subsidiary of ARYA (the time that the Merger becomes effective being referred to as the “Effective Time”). In connection with the Domestication, on the date of closing prior to the Effective Time, each issued and outstanding Class A ordinary share, par value $0.0001 per share, of ARYA (the “Class A Ordinary Shares”) and each issued and outstanding Class B ordinary share, par value $0.0001 per share, of ARYA (the “Class B Ordinary Shares”) will convert automatically by operation of law, on a one-for-one

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basis, into shares of common stock, par value $0.0001 per share, of New Nautilus (the “New Nautilus Common Stock”).

This opinion is being rendered in connection with the registration under the above-referenced Registration Statement of 111,674,810 shares of New Nautilus Common Stock, representing (a) 15,449,000 shares to be issued to the holders of Class A Ordinary Shares, (b) 3,737,500 shares to be issued to the holders of Class B Ordinary Shares, (c) up to 85,295,562 shares to be issued to the equityholders of Nautilus in connection with the Business Combination and (d) up to 7,192,748 shares that may be issued to equityholders of Nautilus upon the exercise of outstanding options to purchase shares of Nautilus (the “Consideration Shares”).

In connection with the preparation of this opinion, we have, among other things, read:

(a)a copy of the Business Combination Agreement, filed as Exhibit 2.1 to the Registration Statement;

(b)the Registration Statement;

(c)the form of proposed certificate of incorporation of New Nautilus, to be filed with the Delaware Secretary of State (the “Certificate of Incorporation”), in the form filed as Exhibit 3.2 to the Registration Statement;

(d)the form of proposed Bylaws of New Nautilus, to be adopted by New Nautilus in connection with the Domestication (the “Bylaws”), in the form filed as Exhibit 3.3 to the Registration Statement;

(e)the form of proposed certificate of corporate domestication of ARYA, to be filed with the Secretary of State of the State of Delaware (the “Certificate of Domestication”), in the form filed as Exhibit 4.2 to the Registration Statement; and

(f)such other documents, records and other instruments as we have deemed necessary or appropriate in order to deliver the opinions set forth herein.

For purposes of this opinion, we have assumed the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as copies and the authenticity of the originals of all documents submitted to us as copies. We have also assumed the legal capacity of all natural persons, the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered, the authority of such persons signing on behalf of the parties thereto and the due authorization, execution and delivery of all documents by the parties thereto. We have not independently established or

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verified any facts relevant to the opinion expressed herein, but have relied upon statements and representations of officers and other representatives of ARYA and others as to factual matters.

Subject to the assumptions, qualifications, exclusions and other limitations which are identified in this opinion, we advise you that:

1.Upon (i) the effectiveness of the Domestication and (ii) the filing of the Certificate of Incorporation with the Delaware Secretary of State, the issued and outstanding Class A Ordinary Shares and Class B Ordinary Shares will automatically convert by operation of law, on a one-for-one basis, into duly authorized, validly issued, fully paid and non-assessable shares of New Nautilus Common Stock.

2.Upon (i) the effectiveness of the Domestication and (ii) the filing of the Certificate of Incorporation with the Delaware Secretary of State, the Consideration Shares will be duly authorized, validly issued, fully paid and non-assessable.

In addition, in rendering the foregoing opinions we have assumed that:

a)ARYA (i) is duly incorporated and is validly existing and in good standing and (ii) has requisite legal status and legal capacity under the laws of the jurisdiction of its organization;

b)Prior to effecting the Domestication and prior to the issuance of securities by New Nautilus: (i) the shareholders of ARYA will have approved, among other things, the Domestication; and (ii) all other necessary action will have been taken under the applicable laws of the Cayman Islands to authorize and permit the Domestication, and any and all consents, approvals and authorizations from applicable Cayman Islands governmental and regulatory authorities required to authorize and permit the Domestication will have been obtained; and

c)The current draft of the Certificate of Incorporation, in the form thereof submitted for our review, without alteration or amendment (other than identifying the appropriate date), will be duly authorized and executed and thereafter be duly filed with the Delaware Secretary of State in accordance with Section 103 of the DGCL, that no other certificate or document, other than the Certificate of Domestication as required under Section 388 of the DGCL, has been, or prior to the filing of the Certificate of Incorporation will be, filed by or in respect of ARYA with the Delaware Secretary of State and that ARYA will pay all fees and

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other charges required to be paid in connection with the filing of the Certificate of Incorporation.

Our opinions expressed above are subject to the qualifications that we express no opinion as to the applicability of, compliance with, or effect of (i) any bankruptcy, insolvency, reorganization, fraudulent transfer, fraudulent conveyance, moratorium or other similar law or judicially developed doctrine in this area (such as substantive consolidation or equitable subordination) affecting the enforcement of creditors’ rights generally, (ii) general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing, (iv) public policy considerations which may limit the rights of parties to obtain certain remedies, (v) any requirement that a claim with respect to any security denominated in other than U.S. dollars (or a judgment denominated in other than U.S. dollars in respect of such claim) be converted into U.S. dollars at a rate of exchange prevailing on a date determined in accordance with applicable law, (vi) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit and (vii) any laws except the DGCL. We advise you that issues addressed by this letter may be governed in whole or in part by other laws, but we express no opinion as to whether any relevant difference exists between the laws upon which our opinions are based and any other laws which may actually govern. We do not find it necessary for the purposes of this opinion, and accordingly we do not purport to cover herein, the application of the securities or “Blue Sky” laws of the various states to the issuance of the Securities.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. We assume no obligation to revise or supplement this opinion should the DGCL be changed by legislative action, judicial decision or otherwise.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the Registration Statement. In giving this 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.

Very truly yours,

/s/ KIRKLAND & ELLIS LLP