Felix,
It depends on whether you want to use the strobe in TTL mode or not. You have 3 options:
1. If you use the sync cord to connect the C5050 to the DS-125 then it'll only work in manual mode only. This means that you can select 3 power settings (1/2, 1/4 and 1/8) on the strobe to control your exposure. Each power setting = 1 f-stop. I think you can do a full dump (1) as well if you set the flash mode on the C5050 to 'slave', but I'm not 100% sure if it sends the signal to the hotshoe in 'slave' mode. Best check with Ikelite. Advantage of using the sync cord in this instance is that you don't have to worry about aiming a slave sensor to the C5050s built-in flash.
2. If you use the TTL slave sensor then you can use the strobe in TTL mode + manual mode as explained above. You will need to make sure the sensor is aimed at the C5050s built-in flash so it can trigger the strobe.
3. If you use the Manual slave sensor then you can use the strobe in manual mode only with 10 power settings in half-stop increments. You can hook up the controller either by using the sensor to trigger the strobe or by attaching a sync cord to it from the camera/housing bulkhead.
Hope that's clear.