You have a T5 that is still in effect at the time of your arrival and your passport will expire before the T5 expires.
The controlling reference for this situation is found in Paragraph 21 of the UK Immigration Rules. It says...
The leave to enter or remain in the United Kingdom of the holder of a
passport or travel document whose permission to enter another country
has to be exercised before a given date may be restricted so as to
terminate at least 2 months before that date.
Source: General provisions regarding entry clearance, leave to enter or remain in the United Kingdom (paragraphs 7 to 39c).
So, they will not remove you from port, but they will be entitled to curtail your T5 to expire in February (two months before your Canadian passport expires). Curtailing your T5 to February will regularise you to the policy that passports should remain valid during one's stay. During the interval between your arrival in January and your T5 expiry, you will be expected to obtain a new Canadian passport, presumably from the Consular Services Section at the Canadian High Commission in London.
This is standard procedure for people who have visas extending beyond the validity of their passport. The key word in the law is "may". The decision to curtail or merely issue a verbal warning is fully down to the Immigration Officer who lands you and their decision is final and irrevocable.
You can also, as pointed out in comments and other answers, obtain a new passport before you leave. This would prevent the possible curtailment of your T5.
In either case your T5 will remain valid even when your passport has expired. There is an option to get a transfer of conditions (they put a new entry clearance in your new passport and cancel the one in your old passport), but for a T5 expiring this year, it isn't worth it. To enter and exit the UK, you need to bring two passports...
- Your old passport containing the T5;
- Your current passport
The Immigration Officer assigned to land you will know what to do with the two passports.