Lots of confusion here. First, between “immigration” and “customs”, and second because the OP has mixed up T3and T5 in the recent post.
From the original post, they arrive in T3 on the flight from the US. Then they need to get to T5 for a flight to Inverness. From T3 they will follow the “flight connections” path to the airside transfer to T5 ( a free bus, dedicated to internal “airside” transfers. Airside means you do not go through immigration to enter the country to transfer; you stay in the airport within the secure zone.
But once in T5, you will pass through security, then will go through immigration/passport control (not customs) to reach the gate for the Inverness flight, because they must enter the UK at that point. There is apparently a separate passport control area for this transfer; not a big deal. Luggage if checked through will be picked up in Inverness, where you will “go through customs” ( usually, just a walk through the green door, no more).