Well one can do the airside bus service from T3 to T5 in under an hour, so in abstract terms you should have plenty of time. The bus ride takes about 12 minutes and there can be 10 minutes between services (though I think 7 minutes is the service level). There is a risk, notwithstanding, relating to the separate tickets, and it's up to your mindset (and the CW ticket conditions) as to whether you take on that risk. Personally I would, many would not.

CW does have a separate fast track through T5 security, but the difference is going to be less than 5 minutes.

Landside always takes longer, involves a passport check and less frequent services between terminals. In 2 hours 45 mins it is still do-able, but I would not do it.