I've made that connection a lot. If you are on hand baggage, or check bags through, it's fine. Just get to the Heathrow express quickly. If you arrive and there is 14 minute wait to next train due to just missing latest one, and then there is a slow security line in t1, you don't have a lot of time and go pretty much straight to boarding.

If you are collecting bags at t5 and then checking in again at t1, you're cutting it fine with zero margin for error. I would give myself a 3 hour gap minimum in this scenario. Did over 100 US to BHD transfers via t5/t1 in past couple years and wouldn't risk any less time than this if I really had to collect bags at t5.

HTH