A bad, worn out clutch will start slipping at max torque range - first in higher gears (5th, 4th), than - if you don't change it - it will do it in lower gears too.
If you really have a clutch that bad, you should notice that the RPM will raise fast but the speed will only follow slowly (if at all up the hill). It feels a lot like driving an auto.
I once had a clutch that bad in my old '88 Subie (1800 GL) and I know that it's possible. I just thought that it's too obvious to mention.