Yes, this will work for the 5200. Same AC adapter for Dymo RHINO Pro 3K, 4K, 5k, 6K anyway.
Does this work on the Rhino 4200?
This charger should work with the 4200. The voltage/current requirements as best I can determine are the same. Both 5200 and 4200 use 6-1.5v AA batteries and the charger is rated at 9v,2 amps.