Yes i calculated it and chose 25mm to be safer there, with 20mm it eouldnt be possible. It will be arround max 1100mm but including end-machining.
The other option would be to take 10mm pitch and gear the servo down with belts 2:1
I would then have a max of 1500rpm on the screw.
Noise is really a big concern for me but i never worked with bigger 5mm screws so i cant estimate the impact on sound.
My 10mm screws, if lubricated, free of chips and mounted properly were always quite ok.

Lower pitch = more ball movement/rpm = more sound?