LHR landside terminal transfers are simple between 123 and 4 as well as 123 and 5. It is a nightmare between 4 and 5

I would suggest you drive to 4 to drop your sister off (or park in short stay and accompany her into the terminal if you have to) and then drive to T5. It is will be faster.

A one way transfer between 4 and 5 is bad enough; a return is too horrible to contemplate.