I have stayed many times at the Premier Inn T4 (it is cheap!) but to get from there to T5 without using a taxi is a bit of a trek. 10 min walk to T4, free train to T2/3, free train to T5. On paper it looks easy enough but the last time I did it it took me 45 mins to get from the hotel to check in T5. I will still do it if I have plenty of time but IMO Premier Inn T4 or the HGI T4 is not an option if time dependent unless you are happy taking a taxi.