Primers
I found two cases (bricks?) of Winchester large rifle primers that I bought sometime ago. I don't know how long ago, maybe ten years. They've been stored in the closet, garage, storage unit, and again in the garage over the time I've owned them. Think they might still be good? I'd hate to load up some rounds and find the primers are duds.
Primers
In 2002 my late brother gave me 5000 Winchester large rifle primers that had been stored about like you described- for 10-15 years before that. I'm still using them and they've been fine.
Primers
I'm still using CCI LR primers that came in the old green packaging...dating back to the 60's. They have a long shelf life. If you are concerned, prime a case or two w/o powder & bullet and fire it (with due caution). I'll bet they go bang.
Primers
If you do what Cherokee said and the primer backs out of the pocket don't be concerned . This is normal. Without powder to push the case backwards the blast of the primer will back the primer cup from the primer pocket. This why if you are making wax slugs you need to open up the flash hole. J.michael
Primers
I have several older packs of primers of unknown vintage, some probably out of the '50s, with dubious storage. So far every one has gone bang, though I would probably use fresh primers if the loads were ones that I was planning to use for self defense.
Out where you live...
humidity is not likely to be a problem. Unless you know they were stored in a humid/oily environment there's not likely to be much cause for concern. We've come a long way from the old mercuric primers that'd go bad as the mercury leached into the brass.
Primers
I wouldn't give them a second thought unless it was life & death.