Should be fine. I am still loading some double base powder that I bought 25+ years ago; it has traveled from Georgia to Alaska and coast to coast in the lower 48, coming to rest here in the MidWest where I am slowly shooting it up. According to my records It chronographs the same as it did new. I have a bit of single base that is older than that and it looks and smells fine. I have some WWII ammo that shoots fine (but it does have corrosive primer compound, fwiw). I've even fired WWI 45ACP and 9mm and it shot just peachy (the 9mm was a little hot, actually, but burned clean as a whistle. Just how they loaded it back then). Your 5 year old powder should be fine.

And smokeless powder has no affinity for water afaik - it should not appreciably absorb any moisture from the air. (Black powder can, of course - again, I have some DuPont FFF that is really old, but it shoots fine in a cap and ball revolver of mine - apparently the original cans do a good job. I'm down to my last 1/2 can of the DuPont stuff...)