Exhibit 5.1

Orrick, Herrington & Sutcliffe LLP

The Orrick Building

405 Howard Street

San Francisco, CA 94105-2669

+1-415-773-5700

orrick.com

November 6, 2019

Twist Bioscience Corporation

681 Gateway Blvd

South San Francisco, CA 94080

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

At your request, we have examined the Registration Statement on Form S-3 (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) relating to the offering from time to time, pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act of 1933, as amended (the “Securities Act”), by Twist Bioscience Corporation, a Delaware corporation (the “Company”), of the following securities: (i) common stock of the Company, $0.00001 par value per share (“Common Stock”), including Common Stock that may be issued upon conversion of the Debt Securities (as defined below) or the exercise of Warrants (as defined below); (ii) preferred stock of the Company, $0.00001 par value per share (“Preferred Stock”), including Preferred Stock that may be issued upon conversion of the Debt Securities or the exercise of Warrants; (iii) senior debt securities of the Company (“Senior Debt Securities”); (iv) subordinated debt securities of the Company (“Subordinated Debt Securities” and, together with the Senior Debt Securities, “Debt Securities”), (v) warrants to purchase Common Stock, Preferred Stock or Debt Securities (“Warrants”); and (v) units of the Company comprised of any combination of Common Stock, Preferred Stock, Debt Securities or Warrants (“Units”).

The offering of Common Stock, Preferred Stock, Debt Securities, Warrants and Units (collectively, the “Securities”) will be as set forth in the prospectus contained in the Registration Statement (the “Prospectus”), as supplemented by one or more supplements to the Prospectus (each, a “Prospectus Supplement”). The Senior Debt Securities will be issued pursuant to an indenture between the Company and a trustee to be appointed in the future (a “Trustee”) in the form filed as Exhibit 4.5 to the Registration Statement, as such indenture may be supplemented from time to time (the “Senior Indenture”). The Subordinated Debt Securities will be issued pursuant to an indenture between the Company and a Trustee in the form filed as Exhibit 4.6 to the Registration Statement, as such indenture may be supplemented from time to time (the “Subordinated Indenture”).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or Prospectus, other than the validity of Common Stock and Preferred Stock and the enforceability of Debt Securities, Warrants and Units.

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We have examined the originals, or copies identified to our satisfaction, of such corporate records of the Company, certificates of public officials, officers of the Company and other persons, and such other documents, agreements and instruments as we have deemed relevant and necessary for the basis of our opinions hereinafter expressed. In such examination, we have assumed the following: (a) the authenticity of original documents and the genuineness of all signatures; (b) the conformity to the originals of all documents submitted to us as copies; and (c) the truth, accuracy and completeness of the information, representations and warranties contained in the records, documents, instruments, and certificates we have reviewed.

Based on and subject to the foregoing, and assuming that: (i) the Registration Statement and any amendments thereto (including post-effective amendments) will have become effective and comply with all applicable laws; (ii) the Registration Statement will be effective and will comply with all applicable laws at the time the Securities are offered or issued as contemplated by the Registration Statement; (iii) one or more Prospectus Supplements will have been prepared and filed with the Commission describing the Securities offered thereby and will comply with all applicable laws; (iv) the Board of Directors of the Company, or a duly authorized committee thereof, shall have taken such action as may be necessary to authorize the issuance and sale of such Securities, and if applicable, establish the relative rights and preferences of such Securities, or other terms of such Securities, in each case as set forth in or contemplated by the Registration Statement and any Prospectus Supplements relating to such Securities; (v) all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate Prospectus Supplement; (vi) a definitive purchase, underwriting, or similar agreement with respect to any Securities offered or issued will have been duly authorized and validly executed and delivered by the Company and the other parties thereto; (vii) any Securities issuable upon conversion, exchange, or exercise of any Security being offered or issued will be duly authorized, created, and, if appropriate, reserved for issuance upon such conversion, exchange, or exercise; (viii) there shall not have occurred any change in law affecting the legality or enforceability of such Security; (ix) that any warrant agreement relating to the Warrants will be duly authorized, executed and delivered by all parties thereto other than the Company; and (x) none of the terms of any Security to be established subsequent to the date hereof, nor the issuance and delivery of such Security, nor the compliance by the Company with the terms thereof will violate any applicable law or will result in a violation of any provision of any instrument or agreement then binding upon the Company, or any restriction imposed by any court or governmental body having jurisdiction over the Company, we are of opinion that:

1. The Common Stock will be validly issued, fully paid and nonassessable at such time as: (a) the terms of the issuance and sale of the Common Stock have been duly authorized by appropriate action of the Company; and (b) the Common Stock has been duly issued and sold as contemplated by the Registration Statement, the Prospectus and any Prospectus Supplement relating thereto.

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2. The Preferred Stock will be validly issued, fully paid and nonassessable at such time as: (a) the terms of the issuance and sale of the Preferred Stock have been duly authorized by appropriate action of the Company; (b) a statement with respect to the shares establishing the Preferred Stock shall have been filed with the Secretary of State of the State of Delaware in the form and manner required by law; and (c) the Preferred Stock has been duly issued and sold as contemplated by the Registration Statement, the Prospectus and any Prospectus Supplement relating thereto.

3. The Senior Debt Securities (including any Senior Debt Securities duly issued upon the exchange or conversion of any Senior Debt Securities that are exchangeable or convertible into another series of Senior Debt Securities) will constitute valid and binding obligations of the Company, at such time as: (a) the forms and the terms of the Senior Debt Securities and their issuance and sale have been approved by appropriate action of the Company, and the Senior Debt Securities have been duly executed and delivered by the Company and authenticated by the relevant trustee, in accordance with the Senior Base Indenture or a supplemental indenture thereto; and (b) the Senior Debt Securities have been issued and sold as contemplated by the Registration Statement, the Prospectus and any Prospectus Supplement relating thereto and the Senior Base Indenture or a supplemental indenture thereto.

4. The Senior Subordinated Debt Securities and Junior Subordinated Debt Securities (together, the “Subordinated Debt Securities”) (including any Subordinated Debt Securities duly issued upon the exchange or conversion of any Subordinated Debt Securities that are exchangeable or convertible into another series of Subordinated Debt Securities) will constitute valid and binding obligations of the Company, at such time as: (a) the Subordinated Base Indenture, in substantially the form filed as an exhibit to the Registration Statement, has been duly authorized, executed and delivered by the Company and the relevant trustee; (b) the forms and the terms of the Subordinated Debt Securities and their issuance and sale have been approved by appropriate action of the Company, and the Subordinated Debt Securities have been duly executed and delivered by the Company and authenticated by the relevant trustee, in accordance with the Subordinated Base Indenture or a supplemental indenture thereto; and (c) the Subordinated Debt Securities have been issued and sold as contemplated by the Registration Statement, the Prospectus and any Prospectus Supplement relating thereto and the Subordinated Base Indenture or a supplemental indenture thereto.

5. The Warrants will be valid and binding obligations of the Company at such time as: (a) the terms of the Warrants and of their issuance and sale have been approved by appropriate action of the Company and the applicable warrant agent; and (b) the Warrants have been duly executed, authenticated and delivered in accordance with the applicable warrant agreement.

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The opinions set forth in paragraphs (3), (4) and (5) above are subject, as to enforcement, to (a) the effect of bankruptcy, insolvency, liquidation, receivership, moratorium, reorganization, fraudulent conveyance or similar laws relating to or affecting the rights of creditors generally; (b) general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith, fair dealing, and the rules governing the availability of specific performance or injunctive relief, whether enforcement is sought in a proceeding in equity or at law; and (c) provisions of law that require that a judgment for money damages rendered by a court in the United States be expressed only in United States dollars.

We express no opinion as to laws other than the laws of the State of New York with respect to the opinions set forth in paragraphs (3), (4), and (5) above and the General Corporation Law of the State of Delaware (including the statutory provisions, all applicable provisions of the Delaware constitution and reported judicial decisions interpreting the foregoing) with respect to the opinions set forth in paragraphs (1) and (2), and we express no opinion with respect to the applicability thereto, or the effect thereon, of the laws of any other jurisdiction or, in the case of Delaware, any other laws, or as to any matters of municipal law or the laws of any local agencies within any state.

We hereby consent to the reference to us under the heading “Legal Matters” in the Prospectus and to the filing of this opinion as Exhibit 5.1 to the Registration Statement. By giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act and the rules and regulations promulgated thereunder.

Very truly yours,

/s/ ORRICK, HERRINGTON & SUTCLIFFE LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP