Eyefinity is the technology that allows you to use more than 2 monitors off of a single video card. To "use" it, you'll need 3 or more monitors, depending on how many video outputs (more specifically, how many Displayports) your specific GPU has. In your case, the 5830 has 3 or 4 video outputs (most have 4, but some have 3), but they all have only 1 displayport, which means your maximum amount of supported monitors is 3 in either case.
The 5830 you have most likely has either:
2 DVI's
1 HDMI
1 Displayport
Or
1 DVI
1 HDMI
1 Displayport
Either way, since you only have 1 displayport, your maximum amount of monitors is 3, EVEN IF YOU CROSSFIRE.
NOTE: Every monitor connected to a single GPU, after the 2nd, requires use of the Displayport output. If your monitor doesn't have a Displayport on it, you will need an ACTIVE displayport adapter if you wish to use it as your 3rd (4th/5th/6th) monitor. Passive adapters will not work!!
Example
I have 1 monitor via HDMI and 1 via DVI. My 3rd monitor will require use of the displayport.
Another example:
I have 4 monitors. But my card only has 2 DVI slots, 1 hdmi, and 1 displayport. I can only use 3 monitors because I only have 1 displayport.
Last example:
I have crossfired 5830's. I CANNOT use any of the outputs on any of the second/third/fourth video cards. All of the monitors must be connected to the first GPU. This is a limitation of Eyefinity, and doesn't reflect on how SLi works, as it is different.