Accessing T3 lounges in LHR on a long layover and leaving from T5 then.

I am traveling DFW to SIN in a few days on AA from DFW to LHR which shows landing T3 and then BA from LHR to SIN from T5. I am wanting to access the Cathay/Qantas lounge on my 5 hour layover in LHR for sometime and then make my way over to T5 for departing flight. Is this doable in LHR? I appreciate your responses and recommendations in advance.