The regular edition 5870 can run up to 3 monitors, 2 DVI/VGA/HDMI and one DisplayPort. You cannot use 2 DVI/VGA and one HDMI as the 5870 can only generate two DVI/HDMI/VGA signals at a time. It will detect the third monitor if connected this way but you'll only be able to enable 2 at a time.
For all 3 monitors, one display has to have a DisplayPort connection either with a DisplayPort monitor or an ACTIVE
DisplayPort adapter. A passive adapter will not work as the 5870 cannot generate more than 2 DVI, HDMI, or VGA signals and a passive adapter relies on the card to generate the signal while an active adapter uses a converter chip to create the signal from a native DisplayPort signal. In my setup I'm using a Sapphire DisplayPort to VGA adapter for the third monitor and I really can't tell a difference at 1920x1080.
All DP to VGA adapters are active, DisplayPort does not have a compatibility mode for VGA and thus all DP to VGA adapters have to have a converter chip. This is probably the best way to get Eyefinity as a DP to VGA adapter is $20 and an active DP to DVI adapter is $100 and uses a USB port for extra power.