GDDR5 is simply the type of memory the graphics card uses for it's on board calculations. It's a graphical iteration of the DDR standard, works a lot faster than typical DDR memory found on motherboards in the main system to provide large bandwidth to the GPU for parallel calculations.
But yes, as long as you have a PCI-E x16 slot on your motherboard (unless its REALLY old, then the answer to that is yes), your graphics card will work just fine.
Sorry for the double post, but i only just saw that question about eyefinity!
Eyefinity is the name ATI gives to cards than can support multiple monitors. A typical ATI card will support Eyefinity up to 3 monitors, the higher end ones can support up to 6.
So basically, you have 3 monitors, plug one in via the graphics card's DVI port, one through the HDMI port and the last one through either the DisplayPort or the D-Sub port (more likely to be DisplayPort). You will then get a triple monitor display off one graphics card.