ATI Radeon 5770 Eyefinity - three monitors

On AMD Eyefinity Technology, there is this remark at the bottom:

Driver version 8.66 (Catalyst 9.10) or above is required to support ATI Eyefinity technology and to enable a third display you require one panel with a DisplayPort connector.

Do you have one screen connected with DisplayPort?

This cannot be solved with a passive adapter. Issue is in hardware and comes down to signaling on DVI, HDMI and DisplayPort.

If I recall correctly DVI and HDMI require an own clock signal per output. Because DisplayPort is a package protocol it requires only one clock signal per card. ATI Radeon HD 5000-series has two clocks for DVI/HDMI so it is possible only to use 2 of those devices, adapters do not change this fact.

There is however an active adater, that allows you to transform DisplayPort signal to DVI-signal. More information about the device here

So what you need is a native DisplayPort monitor or an active device that transforms DisplayPort signal to DVI/HDMI.