You can use contactless/Oyster at T5 to either use the TfL service or connect to it at T2/3.
You can also use contactless/Oyster to transfer between terminals for free, saving the use of a blue ticket that can't be recycled. It's annoying that Heathrow are trying to prove they are becoming more environmentally friendly but now use hundreds, if not thousands, of unrecyclable tickets for free transfers...