Originally Posted by
thesaints
I have done it with plenty of time. In fact, I was arriving at T4 (longer connect to T5 than from T3), showered at Yotel and even had time to visit the BA lounge in T5, although briefly.
Caveat: I did not have checked baggage to wait for, nor to re-check.
Timeframe was similar to yours: 10-ish AM arrival and 1pm departure.
Due to construction right now, T5 security is a bit of a mess.