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.

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.

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.

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.

I wouldn't give them a second thought unless it was life & death.