Personally I wouldn't fly anywhere in the world to see an airport terminal building.
I fly because it's quicker than any other transportation method and I don't want to spend a few days traveling (or maybe weeks).
So why would you spend an extra 2-3 hours just to see an airport. It's nothing special, although at this time it's the best UK terminal in many ways.
Probably when you book your next award long haul holiday then you can use BA and T5.