Did HPC to T5 recently, on the tube.
One thing not yet mentioned is the down escalator at HPC is under repair so out-of-action. Stairs down it is, and a bit of a pain; worse with luggage or in rush hour.
We were against the rush too. I would not be happy taking tube with the rush anywhere starting a journey.

So that'd be Bus/Taxi to PAD and then the HEX. But, Taxi area at PAD is kaput too for 15 months or so. Given OP is without luggage I'd ask the cabbie to drop me off close, not right at the door. Its a 10-15 minute ride in the Friday rush.

Personally ... the lure of the T5 lounges ensures I'm waaay in front of conformance. It is all so easy to get a transport snarl up and lose 30mins.