What cabin are you flying in to LHR? If it's WT+ or above you may be able to sweet talk your way in on the basis that you just earned the qualifying TP. I don't know what success you'll have, but you can ask nicely. If you're in J you'd be able to leave security and go to the Arrivals Lounge.

There's restaurant bar on the far end of T5 past shopping. You may be able to get a semi-quiet table near the window.

Other alternative is to leave security and go find a quiet space in one of the Sofitel restaurants or coffe shops. It's located within T5 premises.