Ok I did some research and saw someone post this:
"Eyefinity requires an ACTIVE adapter to enable a third monitor on HD 5000 cards. Passive will NOT work, except for the first two monitors on the eyefinity 5 and eyefinity 6 cards. For the other three/four monitors, active is still required. A quick explanation of why is because DVI/HDMI requires a special clock, which the card is only able to provide two of. Displayport does not use this clock, so ATI used it as a workaround."
He also explained the difference between Active and Passive adapters:
" This is the big one I have been seeing a lot lately. The difference between active and passive is simple.
Passive adapters are merely a cable to go from displayport to DVI/HDMI/VGA/w.e. The video card detects the monitor as such, and outputs the required signal (DVI/HDMI/VGA). This does require one of the two aformentioned clocks, hence why they do not work with eyefinity cards.
Active adapters, on the other hand recieve a displayport signal from the video card, and convert it to DVI/HDMI/VGA. They will always have some sort of onboard DAC or video converter chip which they use to convert the dp signal. Lately, most everyone has been referring the DAC ones (which are the converters that go DP->VGA) as 'passive.' This is not the case."
So I would say you'd have to get an Active Adapter for you Displayport, and a normal DVI connection, or passive adapter, for the DVI connected screen.