What is the minimum speed a motor vehicle can be operated without violating the law if the speed limit is 25 miles per hour?
There. Is. None.
If there is complete gridlock and traffic is at a standstill, you will not be ticketed for not moving because there is no where to move.
If, however, traffic is travelling smoothly, and you decide to go at 5 mph and are impeding traffic (or 10 mph... or 15 mph), you could be ticketed.
Even on the highway, if there is a posted minimum speed, you are not going to be dinged for dipping below that when traffic is heavy and backed up, nor are you going to be dinged for going slower in a sudden storm where visibility has decreased to nothing.
You are expected to be able to exercise a little common sense, and respond to traffic/weather conditions.