I recently put in an old 5770 along with my GTX 660 since I was only getting about 68 Mh/s, the 5770 alone gets about 380 Mh/s.
With any miner I use, CG, Phoenix, GUIM, the 5770 is shown mining at its normal 380 Mh/s but no shares are ever accepted.
I am using 5770 also and it is working fine.
First. I think there is no problem with the driver and the card, because it is showing a hash rate 380 Mh/s.
Second. What is the setting of your CGminer?