Ammunition does not “expire per se”, but gunpowder loses potency over time. The biggest risk of firing old ammunition is not not not firing, it is the risk that you actually fire the shot and not having enough momentum to get out of the barrel. Proper ammunition storage is crucial for the firearms you rely on in an emergency, such as your concealed firearm. A weapon like that could go for years without being fired.
Although most manufacturers recommend not using ammunition older than ten years, prevention is better than cure. After a few years, he uses those old rounds at the first opportunity, maybe practicing a little at the shooting range. The useful life of ammunition depends to a large extent on the conditions in which they are stored. Most manufacturers guarantee that their ammunition will last at least a decade.
That said, ammunition can easily last more than 10 years if stored under ideal conditions. There are countless stories of surplus military ammunition being used many decades after its manufacture. Ammunition breaks down with age. More specifically, ammunition will lose its effectiveness over time.
There can be several reasons why ammunition breaks down, such as rusty bullets, gunpowder that does not burn, corrosion on the housings due to moisture, etc. It is recommended to replace the ammunition every decade or so. Practically the only way ammunition will spoil is if it gets wet or exposed to enough moisture for moisture to get into the primer. Of course, that takes a while; there isn't much room for water or moisture to pass through, so repeat the exposure what actually makes it happen.
However, the propellant and primer will eventually degrade, but you can maintain its shelf life through proper storage. Yeah, the old ammunition is still worth it. A bullet is fine as long as it can be fired at the shooting range and does not pose a problem for the barrel of your rifle. However, it is better to invest in a newer, hermetically sealed ammunition box.
You can rest assured that shooting will not cause any damage or concern. Ammunition companies are pushing a conservative message, probably because they don't want responsibility if it doesn't shoot (and, hey, they'd like to sell more ammunition). Ammunition manufacturers limit their liability exposure by being more conservative in their estimation of useful life (not to mention selling more boxes of ammunition by encouraging more frequent purchases).