Welcome to the BA forum lkar.

antichef has given some great advice, but here's my take. I'm able bodied so there are going to be aspects I miss, however I do go between T3 and T5 more or less every week, if not more so.

T3 is quite a haphazard building and the layout is such that you may have a short gap between the arrival gate and Flight Connections or quite a long one. There are several long but flat corridors, some with conveyor walkways (I love the French term, tapis roulant). Luck of the draw. Getting from most gates to Flight Connections is flat level, but there are some which involve stairs. In all cases, and most particularly in Flight Connections there are lifts / elevators. In fact the lifts are the easiest way down to the floor level that is necessary to get on the buses. So the bus area is at the ground level of Flight Connections T3. The buses are low level and have a middle door with plenty of marked space for wheelchairs and buggies, but you may have to miss the first bus if there are a lot of passengers on it. There is a small gap between the curb and the bus entrance but I think it is surmountable if everyone is adept. Some staff may suggest you use assistance, but I can well understand why you would prefer to do it under your own steam.

The bus journey takes between 9 and 13 minutes. You then get brought to ground level and curbside to T5. Again there are lifts to take you to T5 Flight Connections. T5 in particular was designed for the use of the physically challenged.

Flight connections in T5 is in two sections, downstairs where you show your boarding pass, upstairs (another lift) for the security check. This is all a very short distance from the bus arrival area. If you know T5: the buses arrive at the foot of the main glass area in departures. The first part of flight connections is directly underneath departures, security - which is the same place as landside North security - is just above departures.

The distances are shorter, and there are fewer steps, going airside. Going landside strikes me as more hassle all over, but it would be the easiest way to try the pods. Well actually, you do have the option, upon arrival airside into T5 to go through the UK Border and go landside directly there too. You could make that decision at the last moment, when you know your timings and can see how long the queue for passports is at T5.

Happy to help with any detailed questions. A direct arrival into T5 would be a lot easier than T3, but I am sure there is the method in the madness!