It's always a conundrum when travel plans are outside the norm, especially when it involves longer periods between flights. Some airports in the world have such 'by the hour' rest hotels where you can shower/eat/nap/sleep/work etc. £125 minimum for 5hrs is a bit steep I'd say, perhaps the only real option is as the OP surmises, to sit and wait it out with distractions in the terminal. Good luck
SHJ