An engineering design problem such as this is done in a series of steps, generally with some iteration in the process. The following is one possible approach:
1) Calculate the maximum load on the top sprocket. Weight of chain, all buckets full, plus estimated chain pretension.
2) Calculate maximum torque on the drive sprocket. Assume that all buckets on one side of the centerline are full, and all buckets on the other side are empty. This is a worst case calculation, not a realistic case calculation. Then add in estimated friction for the nondrive sprocket, plus chain friction. If in doubt, add 50% or so.
3) Calculate RPM. You stated 5 degrees per 15 seconds, so 20 degrees per minute, which equals 0.055 RPM.
4) Calculate a gear ratio. A standard induction motor runs 1800 RPM, the load runs 0.055 RPM, so the initial try gear ratio is 1800 / 0.055 = 32,400:1.
5) You can get a clean design by mounting the drive sprocket directly on the output shaft of the gear reducer. The gear reducer output shaft must have a design radial load rating greater than the maximum load from Step #1. The reducer output shaft torque rating must be greater than the torque from Step #2.
6) Start looking at gear reducer catalogs. Some names to start with include Boston Gear, Rexnord, Alpha, Stober, and Falk. These names are off the top of my head, there are other just as good. You will quickly find standard designs with gear ratios up to 3600:1. You can use a 3600:1 gear reducer if you run the motor through a Variable Frequency Drive (VFD), and run the motor at 11% speed. This step will take a few hours, or more likely, days because industrial gear reducers are available in a huge number of configurations. The gear reducer catalog will have information on drive torque and power at the rated output torque. Those numbers take into account the reducer friction, which can be significant in a high ratio reducer.
7) Now you can choose a drive motor and VFD for that motor. A simple low speed system such as this can be driven by a standard induction motor. No need for acceleration calculations, just turn the motor on and off to operate it.
8) The reducer will almost certainly be a double reduction worm gear. It will be self locking, so turning off the motor will stop it from moving. Cutaway view of a double reduction helical / worm gear reducer is shown below. The motor is fastened to the flange on the upper right, the output shaft is lower left in front: