There's no RAW about the matter AFAIK, so it's up to the GM. For instance, in my case, a character needs a number of X hours of sleep (X depending of several factors) in order to regain all his PPs. If he sleeps less than X hours, he regains zero points.
So, IMO, in your case of five hours out of eight needed, for a character with a maximum of 24 PPs who spent 8 PPs, a GM may choose:
* grants zero power points (= it's all or nothing),
* grants 5/8 of the spent power points, therefore 5 PPs (= one always needs to sleeps eight hours to recover all spent PPs),
* grants 5/8 of the maximum power points, therefore 15 PPs (= the less PPs spent, the less sleep needed).