You won't be able to output 5mV directly. You will probably need to use voltage divider (resistors) to achieve it.
I can't find the source anymore, but the Due's DAC only output from 1/6 to 5/6 of the full (0 to 3.3V) voltage range.
Hence analogWrite(DAC1, 0); would correspond to 0.55V, and it goes up to 2.75V (ish)
Noise will depend on how much current is drawn, as well as EMF and capacitors you use. From my experience this should be a few millivolts, but it also depends on what you are making your Due compute (timer interupts, etc)