When I used to stay at the T5 Hilton twice a week, I always used Windsor Cars for transfer from/to T2 and T5 - I believe it was 18 or 20 GBP one-way to T2 and less for T5, and always very reliable. Should be similar price from T5 to T3.
I used to just call up on +44 (0) 1753 677677 to book, and recommend booking the night before.

Hope this helps