You can't ordinarily go between terminals at LHR, so no, you can't leave T5 to visit a T3 lounge.
How were you planning on accessing the AA lounge? If it's by class of travel or status then there are better BA lounges available to you in T5 than the AAdmirals club in T3. If you only have a AAdmirals club membership you're going to be out of luck.