December 13, 2018

Aptose Biosciences Inc.
251 Consumers Road, Suite 1105
Toronto, Ontario M2J 4R3

Dear Sir/Mesdames:

This opinion is furnished to Aptose Biosciences Inc. (“Aptose” or the “Company”), a corporation incorporated under the laws of Canada, in connection with the preparation and filing with the United States Securities and Exchange Commission (the “Commission”) under the United States Securities Act of 1933, as amended (the “Securities Act”), of the Company’s Registration Statement on Form S-8 to be filed on the date hereof (the “Registration Statement”) relating to 2,705,000 common shares of the Company (the “Shares”) issuable upon the due exercise of options granted pursuant to the share option plan of the Company, as amended (the “Option Plan”) and the vesting of restricted stock units granted pursuant to the 2015 stock incentive plan of the Company (the “RSU Plan” and, together with the Option Plan, the “Plans”).

As counsel, we have made such investigations and examined the originals, or duplicate, certified, conformed, facsimiled or photostatic copies of such corporate records, agreements, documents and other instruments and have made such other investigations as we have considered necessary or relevant for the purposes of this opinion. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates of public officials, certificates of officers, or other representatives of the Company, and such other documents as we have deemed necessary or appropriate as a basis for the opinion set forth herein.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed, photostatic, electronic, or facsimile copies and the authenticity of the originals of such documents. In making our examination of executed documents or documents which may be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and execution and delivery by such parties, of such documents and that such documents constitute or will constitute valid and binding obligations of the parties thereto.

In connection with our opinions expressed below, we have assumed that, at or prior to the time of the issuance of any such Shares, the authorization to issue the Shares pursuant to the Plans

page 2

will not have been modified or rescinded by the Board of Directors of Aptose and there will not have occurred any change in law affecting the validity or enforceability of such issuance of Shares. We have also assumed that neither the issuance of the Shares, nor the compliance by Aptose with the terms of the Plans, will violate any applicable federal, provincial or state law or will result in a violation of any provision of any instrument or agreement then binding upon Aptose or any restriction imposed by any court or governmental body having jurisdiction over Aptose.

The opinions expressed herein are limited to the federal laws of Canada (the “Applicable Law”).

Based upon and subject to the foregoing, we are of the opinion that the Shares, when issued (i) upon the exercise of options in accordance with the terms of the Option Plan and any relevant agreements thereunder and upon payment of the consideration provided therein to the Company; and (ii) upon the lapse or waiver of restrictions and the restriction period relating to the restricted stock units in accordance with the terms of the RSU Plan and any relevant agreements thereunder; will be validly issued as fully paid and non-assessable common shares of the Company.

We hereby consent to the filing of this opinion with the Commission as an exhibit to 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 the Securities Act or the rules and regulations promulgated thereunder. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes of the facts stated or assumed herein or any subsequent changes in Applicable Law.

Yours truly,

/s/ McCarthy Tétrault LLP

	McCarthy Tétrault LLP 500 Grande-Allée Est, 9e étage Québec, QC G1R 2J7 Tel: 418-521-3000 Fax: 418-521-3099