Thank you for your answer.
My lathe has prismatic ways not linear ways with bearings.
So you suggest me to go with 3205 ballscrew and direct driving with coupler ?
1000rpm*5mm = 5m/min rapids is 5m/min good linear rapid speed for a lathe ?
Because my servo is 3000rpm with this setup i will get max 15m/min rapids but the question is if the ballscrew can rotate at 3000rpm without problems.

Because of ballscrew inertia higher pitch ballscrew (10mm) at lower rpm and gearing down would be better ?
If i gear down what pulleys-timing belts will eliminate backlash ?