score:5
You should not be going through Customs, if your bags are checked through to the US. If your itinerary is on a single booking, then your bags should be checked through; double check this when you check in and drop off your baggage at the airline counter at the start of your trip.
Heathrow has airside transit between all terminals; it's not even necessary to clear immigration if you have to change terminals.
Simply follow the purple Flight Connections signs when you get off your plane. If your departing flight is in another terminal, you'll be directed to a bus stop where you will take a bus to your departure terminal. Either way, you will then go through departure security, have a chance to visit the airline desk if you need to, and then be at your departure gate.