What is the shelf life of powder and primers if kept in a cool place? I have several cans that several years old. I have several thousand primers as well.

Can I still use them?

Hybrid animal... If the conditions were stable temperature and relatively dry air several years should have no effect what so ever. I shoot and use components which are in their teens with no problems what so ever. If you chronograph some of your loads, keep records and compare results.

I've got stuff layin around here, powder and loaded ammo that dates back 20-30 years. It functions just fine. As long as it is stored in moderate temperatures and is dry you're good.

The one thing that will ruin this kind of stuff is extreme heat, like a hot garage, attic, or storage shed.

I've got powder stored outside for 40 years, and it still works great!

I've had powder go bad on me. It smelled bad and looked wet so I burned it. It was about twenty years at the time. However I have a can of powder at least 40 years old and it's still good.

Primers have never gone bad on me and I've even got them wet and just sat them in the sun to dry and they was still fine.

Given proper storage, I should think components would last for decades. I've shot bunches of 8X57 that was from the 40s & 50s, and of the duds pulled down, powder and bullets were reused in freshly reprimed brass with good results. I also have a stash of 30-06 from '43 and haven't had a dud yet, but the cans were in better shape indicating they were properly stored.
I've read where Alliant still tests original batches of Bullseye stored under water and that powder has to be well over the century mark by now. Also, I'm still loading vintage IMR 4350 from lot # 72 with no problems at all.