there is a bus to staines roughly every 90 minutes. i say bus, its more a people carrier

https://bustimes.org/services/442-he...l-moor-staines

an alternative would be tube to hatton cross then the 285 to feltham station and then a train to staines. this would be fairly frequent
i don't think there is a direct bus from t5 to feltham station

or its about a 3.5 mile walk.

other alternatives ... heathrow express to paddington, tube to edgware road, big m&s by the tube station

railair bus to reading, big m&s 5 minutes walk from the station