Welcome to FlyerTalk Rickylucas26!!

Basically, you clear immigration, collect you luggage, clear customs and then recheck your bags at your connecting airline's counter in T5.

Exit T5 with your carry on and catch the tram from T5 to T3 (the next stop). Assuming you have your boarding pass, at T3 you go straight to security and then on to your gate.

There are several threads on related topics in this forum (immigration wait times, what to do etc). You can find these by using the forum search function.