There are some incorrect answers in this thread..
there is nothing to stop a BA T5 passenger from using the
airside connection to go to T3 and use the lounges there before returning
airside to T5 for the flight
the confounding issues are (a) having the time to do it and (b) maintaining your BA ready to fly (aka conformance) status.
what you cant do is have a departing T3 flight and go and use the T5 lounges.
See just one of the many threads on the BA board on this subject especially post 3
T3 Access with T5 boarding pass