You could buy a fully flex fully refundable one way out of T5 before the date you arrive, and then you get the BP for a T5 flight.

Then you could state that your travel plans were uncertain, and now you need to go to T3.

If you "must" stay airside for Immigration reasons, I see no reason why they wouldn't get you back to the T3 transit bus.....

Still it's much less complex to just enjoy the T3 F lounge, which isn't far from the CCR in terms of quality and is much quieter than the T5 F lounge.