You can travel by Underground ("Tube") from Heathrow T5 to Paddington. For the easiest journey with luggage, you would need to change trains twice, but the changes are simple and the whole journey is step-free.
Take the Piccadilly Line from T5 and get off at Hammersmith.
Walk across the platform and take a District Line train to Earl's Court.
Again, walk across the platform and take another District Line train (destination Edgware Road - this is important) to Paddington.
At Paddington, the "Way out" sign will take you up some steps into Praed Street. If you want to avoid the steps, follow the signs to the National Rail station. This route has escalators which take you into the main line station. Turn right and then right again up the slope to Praed Street.