Assuming that second pic is what your PSU can output, then you only have 328W for your CPU and GPU. Your CPU is a 95W, and will only take more with an OC. 328 - 95 = 233W, You'll need some 12V power for your mobo and drives, so I'd round this down to 200W. The TDP of the 5850 is 151W. This leaves you with ~50W to spare. I thought the 5850 and 5870 were closer to 200W but I guess I was wrong.
The point is your going to be close. Your calculator link says you need 341W, which you barely have. Same with my guess. You can probably run it, but your going to be using your PSU very close to its maximum output. This is bad for the lifespan of your PSU. Do it, but plan on buying a new PSU as soon as you can.