If you are going this route it would be easier to get a pump and a timer. Harbor Freight has $9 500gph pumps and $10 timers. Even with a $25 water pump this is a better option then having to search for & purchase a motor that will lift ~5 gallons of water and lower it safely in an automated fashion.Then you could run the rope from the pulley to an electric motor.
Then put it on a timer. Fully auto.
so how many times a day would you need to be in there to lift the bucket?