So PHL-LHR is on BA? AA would help if their DEN-PHL flight is late causing you to miss PHL-LHR. They should rebook you all the way to CFU.

But if BA PHL-LHR has a delay I think you will not get rebooked for free in LHR.

Assume you are all US citizens? Immigration can definitely take 1-2 hours at certain times, especially as you are arriving with lots of other US flights. You collect bags after immigration so don't need to consider how long this would take, if immigration is expected to take a while.

Then you go through customs. In the UK it is different and there's no customs form, (provided you don't bring anything that needs to be declared) it doesn't take any time at all unless you are in the less than 1% of people pulled aside for baggage examination.

A LHR T5 to T5 transfer including rechecking bags should be relatively speedy, if you use the machine to print your bag tags yourself. On the other hand, at T5 you must pass through security 35 minutes before departure or you will be offloaded automatically.

So the question is can you recheck bags and get to the security entrance 2h 50m after landing from PHL? I think you probably can most of the time. You need to consider what happens if you don't. Do you have travel insurance that covers this or would you be happy to pay for a new ticket?