So you are planning to go through security at T5 to get airside, then get the transit, take the airside bus to T3, use the lounges there, go through connection security there (no fast track btw), come back to T5, go landside, go through the faff of getting Ready to Fly reset, and then go through security at T5 to go airside for your flight?

Seems like a heck of a lot of effort going on especially in this weather. Why not just go through security at T5 and use the GC lounge in T5B which will be quiet? (if you need to get back to T5A remember to use the walkway on -4 and not the transit on -2)