The HD5770 and HD5750 are able to handle 3 outputs simultaneously. However one of them must be displayport
How many non-DisplayPort monitors can I use with an AMD Eyefinity technology-enabled graphics card?
You can connect up to two non-DisplayPort monitors at one time to an AMD Eyefinity technology-enabled graphics card using non-DisplayPort connections or passive DisplayPort dongles. To enable and drive 3 or more non-DisplayPort monitors at one time, the additional non-DisplayPort monitors must be connected with an active DisplayPort dongle.