Hotels INSIDE London Heathrow Airport at Terminal 5

With your arrival and departure times, I would stay in central London and spend time sightseeing then go back to LHR the following morning.

keep in mind the travel time to the central city area to and from the airport, plus the being at the airport 3 hours before flight.

keep in mind the travel time to the central city area to and from the airport, plus the being at the airport 3 hours before flight.

Only two hours intra Europe.

Personally, I'd stay at Heathrow and, if you really want to try to get into London for a quick visit, take the train to Paddington or Uber into the center and then return that evening so you can sleep in a bit the next day before proceeding on.
The Heathrow Express underground train is a very efficient (and free) way to get between terminals. There's a Premier Inn over at terminal 4 that's quite nice and quite inexpensive. Can recommend it.

It may be too late, but I would say going from central London to central Paris, it is quicker and a lot more comfortable by train (Eurostar).
If you are landing at ~15:00, you could be at a hotel in central London at 17:00- 17.30. Pick a hotel near St Pancras station, then you have an evening and a morning in London.
Eurostar timetable is here: https://content-static.eurostar.com/documents/460888_Timetables%20Core%20Destinations_Issue%2083_EN_0.pdf
For example, 14:22 departure arrive Paris 17:47 (2h25 + time difference) and you are already in the city centre.

Have you thought of staying at the airport and going in to Windsor. Or, even staying in Windsor. It is a lovely, restful place.

I believe the only hotel connected to Terminal 5 is the Sofitel (easily walkable once through immigration). Otherwise, other nearby hotels aren’t quite on-site.