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Exhibit 99.5

CERTIFICATION PURSUANT TO RULE 13a-14 OR 15d-14 OF THE
SECURITIES EXCHANGE ACT OF 1934

I, James Parsons, certify that:

|1. | I have reviewed this annual report on Form 40-F of
      Trillium Therapeutics Inc.;                                                                                                                                                                                                                                                                  
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|2. | Based on my knowledge, this report does not contain any
      untrue statement of a material fact or omit to state a material fact
      necessary to make the statements made, in light of the circumstances under
      which such statements were made, not misleading with respect to the period
      covered by this report;                    
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|3. | Based on my knowledge, the financial statements, and
      other financial information included in this report, fairly present in all
      material respects the financial condition, results of operations and cash
      flows of the company as of, and for, the periods presented in this report;                                                
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|4. | The companys other certifying officer and I are
      responsible for establishing and maintaining disclosure controls and
      procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and
      internal control over financial reporting (as defined in Exchange Act
      Rules 13a-15(f) and 15d-15(f)) for the company and have:

| | a) | Designed such disclosure controls and procedures, or
      caused such disclosure controls and procedures to be designed under our
      supervision, to ensure that material information relating to the company,
      including its consolidated subsidiaries, is made known to us by others
      within those entities, particularly during the period in which this report
      is being prepared;
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| | b) | Designed such internal control over financial reporting,
      or caused such internal control over financial reporting to be designed
      under our supervision, to provide reasonable assurance regarding the
      reliability of financial reporting and the preparation of financial
      statements for external purposes in accordance with generally accepted
      accounting principles;    
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| | c) | Evaluated the effectiveness of the companys disclosure
      controls and procedures and presented in this report our conclusions about
      the effectiveness of the disclosure controls and procedures, as of the end
      of the period covered by this report based on such evaluation; and                                                                                                       
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| | d) | Disclosed in this report any change in the companys
      internal control over financial reporting that occurred during the period
      covered by the annual report that has materially affected, or is
      reasonably likely to materially affect, the companys internal control
      over financial reporting; and                                                                             

|5. | The companys other certifying officer and I have
      disclosed, based on our most recent evaluation of internal control over
      financial reporting, to the companys auditors and the audit committee of
      the companys board of directors (or persons performing the equivalent
      function):
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| | a) | All significant deficiencies and material weaknesses in
      the design or operation of internal control over financial reporting which
      are reasonably likely to adversely affect the companys ability to record,
      process, summarize and report financial information; and
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| | b) | Any fraud, whether or not material, that involves
      management or other employees who have a significant role in the companys
      internal control over financial reporting.                                                                                                     

Date: March 12, 2018/s/ James ParsonsJames ParsonsChief Financial Officer


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