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Exhibit 99.5

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

I, James Parsons, certify that:

1.                  I have reviewed this annual report on Form 40-F of Trillium
Therapeutics Inc.;

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;

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
issuer as of, and for, the periods presented in this report;

4.                  The issuer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 issuer 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 issuer,
  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;

(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;

(c)
                   Evaluated the effectiveness of the issuer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

(d)                  Disclosed in this report any change in
  the issuer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 issuers internal control over
  financial reporting; and

5.                  The issuers other certifying officer and I have disclosed,
based on our most recent evaluation of internal control over financial
reporting, to the issuers auditors and the audit committee of the issuer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 issuers ability to record, process, summarize and report
  financial information; and

(b)                  Any fraud, whether or not material, that involves
  management or other employees who have a significant role in the issuers
  internal control over financial reporting.

|Date: March 9, 2016
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