The hoppas do shut down at night but they stop pretty late seemingly midnight
http://www.nationalexpress.com/coach...20Gatefold.pdf
If you arrive later than this, call your hotel to arrange a minicab, or check on local buses.
do not get a taxi - you'll be hit with surcharges
LHR hotels can be pretty reasonable if booked in advance and pre-paid - £40 or £50 for a night is not uncommon. Try the Holiday Inns, Park Inn and Sheratons (but avoid Holiday Inn M4 - it's the one furthest away).
in the morning, minimum check-in at LHR T5 is 45 minutes (and you need to have entered security by T-35 if you already have your boarding pass). Given the hoppas start around 5 am again, getting there won't be a problem. Just allow a bit extra time for traffic.