The board has a PCIe x16 slot.
If you want to keep it cheap, I suggest either,
http://www.amazon.co...=radeon hd 5450
Radeon HD 5450 about $30 (USD). It's not very powerful, but it'll play TF2 and Minecraft, Keep in mind though that the 64-bit bus will limit the card severely.
or,
http://www.amazon.co...=radeon hd 6450
Radeon HD 6450 about $40 (USD). This should give you better performance, but it probably won't boost your resolution or your AA. Again, it has a 64-bit bus.
Now, you could look on eBay, I got my Radeon HD 4850 for $40 (USD) after shipping, which isn't too bad for a high performance card, even though it is an older model. I won't post any eBay links, though since prices and products are constantly changing. If you look for AMD cards, keep in mind the numbering system. The thousands place is the generation, the hundreds place is the level in the generation, the ones and tens place are the performance level. This means that the 5450 and 6450's biggest difference is how new they are. This also means that an old 3650 will destroy a much newer 5450, but I don't think you'd be insane enough to spend that much money and such an old GPU.
Since you are looking to spend the least amount of money possible, I would suggest you avoid new nVidia cards. AMD has had a better price-to-performance ratio for some time now.
Also, here's a site that compares GPUs. They're all theoretical values, but it'll give you a ballpark estimate as to how a card will perform relative to another.
http://www.hwcompare...d-6450-oem-1gb/
Oh, just for reference, take a look at the service manual and scroll to page 9.
ftp://ftp.dell.com/Manuals/all-products/esuprt_desktop/esuprt_dimension_desktops/dimension-5150x_Service%20Manual_en-us.pdf
Edited by Laser_Lens_4, 18 March 2014 - 02:52 AM.