Originally Posted by jerry a. laska

By separate itinerary, I assume you mean separate tickets? Will you have checked bags? If so, its is my understanding that VS will not check bags through to BA on separate tickets. In that case you would need to pick up your bags and go through immigration in T4 and then make your way with your bags to T5 and check them in with BA. If you have to do this then I would skip the arrivals lounge and head directly to T5. Instructions are in this Guide post:
https://www.flyertalk.com/forum/25935803-post9.html

As you are flying Upper Class on VS if you don't have to collect bags you could go through immigration at T4 and use the arrivals lounge but doing this after retrieving bags is probably not wise. Just watch the time and make sure you provide yourself with plenty of time to make the transfer and to go through security at T5.

If you don't have checked bags (or they are checked though to BA) the easiest transfer would just be to stay airside and transfer to T5 through flight connections. There is no formal immigration but there is a passport check and security if you transfer airside. Again see the Guide post above. At T5 you could then use the lounge.