My cat had 4 kittens 5 days ago and for the past 2 days she keeps wanting to go outside and leave them, should I let her?

Why not? As long as the kittens are in a warm safe place it's OK.
After all, in the wild the mother lions, cheetas etc. leave their litters to hunt. I'd frisk her for a dead mouse before you let her back in tho'.

If nothing else she probably just wants to stretch her legs a bit.