The usable life of ammo is almost indefinite if it's stored in a relatively cool, clean, and dry environment. An average climate-controlled home is fine; ammo will last for decades in this environment. There are folks on this forum who have successfully fired ammo that was made well before WWII and had been stored indoors.
Water or chemical exposure can ruin ammo relatively quickly; extreme heat and high humidity will ruin it too, but it may still take a number of years.
The ammo in your picture is NOT that old, and it looks like it has been stored with care, judging by the appearance of the packaging. I doubt you'll have any problems. Fire away.