Probably a better question for the BA forum and answered in this thread: https://www.flyertalk.com/forum/brit...ding-pass.html. TL;DR is if you're originating from London you can't enter T3 from landside with at T5 BP, and although there's a convoluted way to get to T3 (clear security at T5, take the train to T5C and back so you end up in the transfer/arrivals channel, bus to T3 and clear transit security there), it's probably not worth the trouble (especially since on the way back the BA T5 IT systems will be confused as to why you're clearing security again). If you're connecting in LHR it's easier but does involve clearing security twice.

Also technically the LHR terminals are connected by airside transfer buses but you need to clear security (no immigration/customs).