If they are asking for all that up front, I would run a mile. Should the school enter any financial difficulty with £5k of your money, you'll never see that money again.
If it's an hourly rate at £131 an hour, that's pretty good. Things they haven't included:
Full student ground pack about £200
Medical, about £100
test about £300
licence issue £150
radio practical, £150?
Petrol to and from the airfield, including wasted trips when the weather wasn't good enough...?
Plus the fact the average PPL is more like 50-60 hours, so whatever the hourly rate is after your initial 45 hours.