Welcome to the BA forum. I’m sure one of the mods will be along with a more formal welcome. The sticky for the BA dashboard at the top of the page is your best place to start for answers to your search, if you haven’t seen it already
https://www.flyertalk.com/forum/brit...dashboard.html
Specifically this thread on the dashboard will help:
https://www.flyertalk.com/forum/british-airways-executive-club/1735255-guide-connecting-lhr-t5.html
To answer your question, no you don’t need to clear security again connecting from a domestic connection ( unless going to a different terminal). Follow the purple flight connections signs and scan your boarding pass to access the T5 A departure lounge and duty free shops. Long haul flights usually depart from B or C gates by transit train, but can occasionally depart A gates via bus- so double check the departure screens