It does sound like your strobe is not firing at the right time, or possibly your camera is set wrong. Does your camera shoot OK without the external flash, using only the internal flash? I found it OK for close subjects, like the thumbnail below.
For a simple test, put your camera in manual mode M, set the shutter to say 1/100 and the lens to f1.8. You should be able to take a photo into a mirror, and see the external flash fire too, in addition to your internal flash. I suggested M mode because then you won't have a pre-flash, which sometimes confuses external flashes.
This flash is weak, guide number 14, so it's really not great for anything but close-ups anyway. But it should help a little over the internal flash, using the external flash as a slave to your internal flash. The C5005 has several flash settings. The one you want is internal plus slave, as I recall, do check that. I used a C5050 a lot, and it's really a gem, but syncing with a flash does require the settings to be correct.
You might also want to do a search for the 5050 here on the board, and also try some settings from this article, which is a great tutorial:
Splashdown Divers - Boynton Beach, Florida - Underwater Digital Photography - 5050 Settings - 5060 Settings