I've just purchased a HP DC5750 minitower. I'm looking for put in a graphics card but down have room for one of the cards that takes up 2 PCI slots at the back (not sure the correct term).
Can you help me pick out the best card that would fit my system?
The card would be aimed at gaming.
Since your computer is a minitower, you have to get what is called a "Low Profile" card, so that it fits in your system. This really limits what you can buy and how much performance you can get. Not to mention your Power Supply is also very weak. There are 4 possibilities listed on the HP website that could have come with your PC.
Integrated ATI Radeon X300 graphics with VGA and DVI-D
ATI Radeon X1300 (256 MB SH) PCIe x16 Graphics Card
ATI Radeon X1300 Pro (256 MB DH) PCIe x16 Graphics Card
ATI Radeon HD 2400XT (256 MB DH) PCIe x16 Graphics Card
If you have the 2400XT, you can't really upgrade from there for any noticeable performance increase. If you have one of the other ones, you could look at getting a HD 4350. It's still not going to be that amazing of a card though, low profile cards are pretty limited, and you power supply just limits the selection even more. Here's a link to the best deal for a 4350 that i could find.