Heathrow airport doesn't provide any sensible transfer between T5 and T4. The trains are intermittent and the journey will take up to an hour though there's no problem with baggage.

And at T4 it isn't so easy to find the Hilton, you have to go upstairs and then turn right and right again to the far corner of the terminal to find the passageway.

A cab driver would be horrified and will quote the minimum £35. Maybe call the Hilton and get them to send a car, or call one of the car-services recommended on this board