Did everyone else just skip over the 5 or 6 axis part and go straight to the belt vs screw discussion?

From what I've seen, the OP didn't say leadscrew or ballscrew. He just said screw.

Also, there has been no mention from the OP about dimensions of the machine. IMO, an important detail to leave out.

No vote for rack and pinion? Depends on machine size, IMO.

I'll vote for the ballscrew. Belts, perhaps the least expensive, perhaps they have a place for hobby machines on a budget, I'm not going to slam that too much. But on a 5 or 6 axis CNC machine? No, they don't belong there.

Perhaps the OP can give more info.