If you’re looking for cheapo LHR hotels then look at any of the ones on the Bath Road - there are lots of options with all major chains represented. It is a ten minute bus ride from T3 and there are frequent public buses - there is a thread on the BA board with the details. As you are departing from T5, it is also worth checking the hotels attached to T4, which are often good value - T4 is connected to both T3 and T5 by (free) trains.