To use Eyefinity, which is ATI's way for 3 monitors on one card, you MUST have either a DisplayPort native monitor or an active converter (which is about $100). All of the 5*** series cards support EF. I have seen people's computer running with eyefinity and it does work, you just have to have a DP monitor or the right converter. A simple DP to HDMI would not work.
Info:
ADAPTER: http://www.overclock.net/ati/581169-5870-1gb-eyefinity-does-not-support.html
EYEFINITY INFO: http://www.overclock.net/ati/581981-offical-ati-eyefinity-info-thread.html#post7269107
Good Luck