This is what I was worried about. However, when we disembarked from the plane there were red envelopes waiting for us. These envelopes were marvellous things; whenever an airport employee saw them, they waved you past the queues.
So in all it took only 15 minutes to get through customs. Of course I then had to collect my hold luggage (apparently you have to do this at your point of entry. This involved picking the case up from the carousel, walking to the exit, handing the receipt (collected from the automatic passport control machine) to the guy at the exit and handing the case to someone just outside the door.
I then had to go up the stairs, catch a tram from Terminal 5 to Terminal 3, go through security again (oops, had a partially drunk bottle of pop in my bag) and then find the gate.
I did reach the plane and was the last person to board with only 7 minutes to spare for take-off.
Couple hours later and ne taxi ride later I am at the hotel.
Only took a total of 22 hours from when I left home to entering the hotel.
I think I need sleep.