4.5 hours in London should be plenty of time as long as you don't have a lengthy delayed arrival.
Border Control is fast. As long you have your ETA you simply use the e-gates (scan passport, have your picture taken) and you are through. Claiming luggage can take the time, but I've never had it take more than an hour.
When you exit arrivals at terminal 5, just take the elevators up to departures. They are automatic and are much quicker than the escalators. You will go through an automated bag drop, have your passport checked and then head through security. Security at Heathrow terminal 5 no longer requires you to take anything our of your bag. You will need to empty your pockets completely! Once through, check the departures board. Don't be surprised if your gate isn't shown yet.
Worst Cast scenarios once the plane has arrived at gate:
Walking to Passport Control, 15 minutes
Passport Control, 15 minutes
Luggage collection and additional 45 minutes
Bag Drop 15 minutes
Security 15 minutes.
I would expect that from the time you leave the plan to making it through security will probably be no more than 2 hours at most.