Is this process different if we’re arriving into T3, and then departing from T5 after a 4-hour layover?

T3 arrival is on Delta and T5 departure on BA on separate tickets. Both international flights.

What is the passenger flow on international arrival at T3 - do you get dumped into the terminal in the shopping zone and have to make your own way to passport control (like in AMS) or are the international arriving passengers segregated from the departing passengers(like most US airports)?

And, if we do have to leave the secure zone on arrival in T3, can we then turn around clear security in T3 showing our T5 boarding passes and indicate we are visiting the Amex lounge?

Thanks for your help!