The Home City is a big part of your economy in AOE3, and it can't generally be attacked. Furthermore, you have some potent economic options late in the game that can enhance your New World economy as well. The comination of both of these features can mean 1000s of resources in Age4.
Now, you can just keep turning those resources into an army. That is a fine strategy, and it does work, and given the high casualty rates of any battles with artillery, it's not too often that you get stuck at the pop cap. But there aren't a lot of other strategies at that stage. If the game goes on long enough, everyone has all the best military and econ upgrades.
Also, the way Age of Empires games are designed, fighting in Age1 is pretty rare (though it gets easier in AOE3 with the right HC upgrades). Age2 raids can be dangerous, and can end games right there, but they are also easy to thwart with the right defenses. That leaves only 2 Ages for most of the fighting to take place in. If you're playing a 40 minute game and hit Age4 in 20 minutes, then you might feel like you've spent half the game without even an option to Age up again.
Hence, the Fifth Age. You can try to leverage your super-powered economy into an attempt to get even better upgrades and try to shut down the game. It's a risk though. While going up to Age3 and Age4 is nearly always a good thing, it's possible to go up to Age5 too soon. All of the Age5 upgrades, while crazy good, are also very expensive. You need a lot of villagers and can't be worried about resources running out soon. I've been in a few games where I wish I could take back my decision to go to Age5 and spend the money on more soldiers instead.
In our 4-6 player games, at least half the players end up in Age4 before the game is over. But seeing someone hit Age5 is much more rare -- maybe 1 in 10 games. But they're memorable games.