(Eh, I'll make an answer post anyway, whatever)
It's probably easiest and cheapest to do this with a minimum of graphics cards, so you don't need a huge case and mobo. There are Radeon HD 7970s that support 6 displays off one card [Note: you would need a ton of Mini-DP to DVI/HDMI adapters since your monitors don't have DP inputs], so you could do this in a decently small enclosure. Or you could put your 5 extra displays on an Eyefinity card and run your main from a separate one for higher performance. If you're going for the lowest possible price, there are multi-GPU solutions that will work as well, but compatibility may be an issue.
And yes, an Eyefinity card can be run in non-Eyefinity mode with 6 separate monitors.
- Up to 6 displays supported
- Independent resolutions, refresh rates, color controls, and video overlays
Edit: As for doing this without an Eyefinity card, Nvidia does appear to support up to 6 total displays, and the GT 640 appears to support 3 simultaneous outputs, so if I had to guess, I'd say the system you described ought to work. (Note that most motherboards don't support enough PCIe bandwidth for 3 graphics cards to run really quickly, though this doesn't matter if you aren't running SLI; your other monitors will all be slow no matter what you do).