I wonder if you could do this on the seriously cheap side... Just get a pour top for the bottle and then some airline tubing and an adjustable airline valve. Just put the bottle in some kind of holder upside down and attach the airline tubing to the pour spout and crank down the valve to only drip at the 5ml per day rate. That would probably be the hardest part, but then you would have a super cheap vodka doser that would drip 24x7.
Might need to dilute it down to get the drip rate set right.