Upvote:5
If you booked this itinerary as a single ticket in a single transaction, then you have adequate time to make this connection (although not a huge amount of time to spare). You do not need to claim your luggage nor pass through immigration, nor do you need to pass through a customs inspection.
When you deplane in Terminal 5, follow the purple signs for "Flight Connections". You will take a bus over to Terminal 3, and then you will clear security in Terminal 3. If you need to claim onward boarding passes, you can do so in Terminal 3. Your baggage will be checked through to your first airport inside the United States.