One of my rigs has 6 x 5770 of various makes - none yours - running cgminer 3.7.2 with this configuration file. Average KHs is 173 per card, with 3-12% rejects.
{
"pools" : [
(omitted)
],
"intensity" : "18,18,18,18,18,18",
"vectors" : "1,1,1,1,1,1",
"worksize" : "256,256,256,256,256,256",
"kernel" : "scrypt",
"lookup-gap" : "0,0,0,0,0,0",
"thread-concurrency" : "4032",
"gpu-engine" : "741",
"gpu-fan" : "0-85,0-85,0-85,0-85,0-85,0-85",
"gpu-memclock" : "1250",
"temp-cutoff" : "95,95,95,95,95,95",
"temp-overheat" : "85,85,85,85,85,85",
"temp-target" : "75,75,75,75,75,75",
"api-mcast-port" : "7701",
"api-port" : "7701",
"expiry" : "120",
"gpu-dyninterval" : "7",
"gpu-platform" : "0",
"gpu-threads" : "1",
"hotplug" : "5",
"log" : "5",
"no-pool-disable" : true,
"queue" : "1",
"scan-time" : "30",
"scrypt" : true,
"temp-hysteresis" : "3",
"shares" : "0",
"kernel-path" : "/usr/local/bin",
}