You should also consider overclocking if you are looking to get a little more out of that old machine along with the card. It has a pretty decent Asus motherboard.
Its not like you should be worried about it wearing out..
Wait.. do you still have 512 mb ram? Upgrading that would be the simplest performance increase you can get.
The FX 5200 that your computer has isn't all that weak of a card considering the age of the system. I had one in my old build and it played UT 2003/2004 surprisingly well.
The problem with upgrading AGP graphics is that because fewer of the cards are sold now AGP graphic cards cost more than their PCIe 16 equivalents. That card i suggested above for $69 sells for $40 in the newer version.
You can get a pretty decent new rig for ~$500... Keep that in mind while you consider spending $70 on a card.