You have 2 strobe control options:
(1) sync cord hard-wired TTL (using Ike's Olympus TTL conversion circuit) with Ike's DS-50 or DS-125 strobes. Using this setup you let the camera automatically decide on what the flash exposure will be ie the camera will control your strobe's brightness. Olympus TTL flash exposure is very good and Ike's conversion has also received good reports from users. However, do keep in mind that TTL exposure itself has its limits and can be fooled by certain situations. In these difficult situations, if you use a DS-125 strobe, you can switch the strobe to manual and get 4-step control (full dump, 1/2, 1/4 and 1/8). Note: since Ike provides a hard-wired TTL solution the TTL sensor (#4100.5) you mentioned in your earlier post is not required for the setup you are looking at.
Or (2) you could opt for full manual control by adding Ike's manual EV controller (#4100.6). By wiring this to your setup you can control the strobe's output manually in 10-step increments. Using this setup you have full-control on your strobe's brightness and exposure but some understanding of flash exposure (ISO, f-stops, guide numbers and strobe-to-subject distance) will be of help. Typically you would make an educated estimation on how bright your strobe should be for the scene, dial it in to the manual controller and take the shot. If the strobe is too bright you dial it down, not enough light you dial it up. With practice and understanding you will be able get good exposures on the first go. The advantage is that in difficult exposure situations where TTL exposure is likely to get fooled you can control the strobe output yourself and get correct exposures.
As with all the good advice you got from other members in your other post, both the C5050 and C5060 are good cameras. The biggest difference is in the way they handle wide angle conversion lenses. With the C5050 you simply screw on the lens underwater when you require it. Add an Inon UWL100 wide conversion lens and you will get about 91° view underwater at the widest. Attach the Inon dome to the UWL100 and you get ~127°. With the C5060 you have to decide before your dive if you will be shooting wide angle. For this you will need to house the Olympus (land) wide conversion lens (WCON-07C) with the Ikelite 3" dome port (#9306.37). This combination will give you ~97° underwater. Or you could use the dome port with just the C5060's standard lens (ie no WCON-07C) and get about 73° at its widest underwater.
HTH