0-5V 1A Dual Output DC Power Supply - SOFTWARE CONTROLLED
You could build an inexpensive supply using a pair of LT3081 positive adjustable regulators.  Unlike other adjustable regulators like the LM317, the LT3081 can be adjusted all the way down to 0V.

Adjustment of the voltage is done via a single resistor, 20k per volt.  So 0 ohms is 0v, 20K is 1V, and 100k is 5V.

For programming, you could use the X9119TV14-2.7 digital potentiometer.  It's maximum value is 100k ohms, which matches the 5V setting of the regulator, and has 1024 steps, which provides 5 mV resolution you specified (most digital pots have only 256 steps or less).