Last year I lived a 10 minute bus ride away from LHR, I can tell you a great place to run around is Stockley Park. I have done a few times and it's a nice surface so long as you have running shoes. It's a business park with some big firms with offices there, alot of pathways and even a pond with a wooden bridge.

Not particularly hilly but good for a quick 5 miler as you've requested from LHR.

To get there just head straight up the 'A437' and it'll be signposted.