Small update: I did a mild ghetto mod, took out the PSU from the Fractal Design Define R3 (has only 7 expansion slots, so when the GPU card is in the last slot, it collides with the PSU) and used the last slot on the mobo (FX890-GD70) for the 3rd 5830. So now I have a empty slot between each of the 3 GPU cards, temperatures are at 75/75/78 at default clocks.

So now I am looking to get new case, probably will go with LIAN LI PC-8FIB as it has 8 expansion slots (as opposed to the Fractal Design which has only 7).

I run all this setup on Corsair AX-750 without problems:

AMD Phenom II 955 X4 Black Edition
NOCTUA NH-D14
MSI 890FX-GD70
4x Corsair 2GB 1600Mhz CL9 DDR3
3x Sapphire 5830 Xtreme
1x WD Velociraptor 300GB
2x Samsung F1 750GB 7200RPM
2x Samsung F2 1,5TB  5400RPM
6x 120mm fans

Please note this is not a dedicated mining rig, I use it for occasional gaming and also serves as home file-server.