Possible Yes. Feasible No.
Assuming that you land on time, and Even if you are fortunate With the the time you need to clear immigration at T5, and then re-clear security and be at the gate in good time for your onward flight
Heathrow T5 to T3 using the free transfer on the train is around 8 to 10 minutes, but there can be a 15 minute wait at some times of the day. There is also a walking tunnel to T3 from the train platform. I would say at least 30 to 40 minutes each way between terminals.
When I last flew from T5 it took 50 minutes to clear security.
Terminal 5 is a fair distance across the airport from the other parts of the complex, and distance is your enemy.