Originally Posted by corporate-wage-slave

If you are a Gold / Emerald cardholder with e-gate access and HBO (or through checked with luggage) then normally this is the fastest way to connect at T5 anyway, until about 16:00 hrs. So yes, simply take the bus to T5 as if staying airside, but once you arrive in T5 exit via the UK Border e-gates out to landside, best to take the right side escalator after passport control. Then take the burnt orange lift to Departures, then go rightwards to the First Wing. After you have done it once, you'll probably never bother with Flight Connections again.

If you look at a map of T5 it's pretty much a straight line to Flounge via the First Wing, as going via Flight Connections security, and shorter if using Fast Track Security since that goes via North.