Like the other posts have said- if the ammo in the boxes are still factory, I wouldn't hesitate. I see Academy stickers on some of those boxes. That isn't what I would call "old"; I don't think that became a chain until the mid-90's.

I've shot a bunch of surplus ammo that all went bang, all much older, and likely went through some rougher storage. If you have 20 year old factory ammo stored in a manner that preserves the cardboard boxes, you should be good to go.