I have a Core2Duo with only 4 megs of ram and an ATI 5830 (the lowest of the 58XX series IIRC) and I can run almost full settings at 1920X1200...
2048 Textures
MAX AA
Sliders set to most detailed and furthest distance
All advanced options on EXCEPT other planes' shadows.
Smooth Shadows enabled, but only 2048 textures.
If you have a 5850 you can probably crank up to 4096 shadow textures, and with a 5870 you can probably enable other planes' shadows as well.
Personally I usually have shadows turned off completely (except building shadows) because it gets a little distracting at times.
Have you read my Aces High guide to graphics settings posted
HERE? (right click/save as)