Short answer is probably yes.

It's hard to say weather the motor will stall without knowing what voltage your driving it from, ideally the specific motor and the drive ratio between the motor and 5mm pitch ballscrew. Just as an example, lets suppose the motor outputs 1.2Nm at the speed you're running it at and it's a 5mm pitch screw with a 1:1 ratio. Use the following formula to find the force the Z-axis can apply:

F=T*2*pi*e/p

(F=Force, T=Torque, e=screw efficiency, p=pitch)

So using the numbers above, F=1.2*2*3.142*0.9/0.005=1357N ... which is a large force. So as you can see, the mechanical advantage from using a screw drive is very high so I'm surprised that it would stall, especially at such low speed. Perhaps the gib strips are too tight on Z? What rapid feedrate do you get?

For the parameters you specified, I'd try about 9mm peck depth and if using 2500rpm at about 200mm/min.