So would this not be possible if they just went with HDMI instead. Why not just make it with 2 DVI and 1 HDMI with none of them shared. How can this be possible with DP but not with HDMI. I guess I just don't understand why they didn't just use 2 DVI and 1 HDMI. Or 3 HDMI ports. And get rid of the DP all together. Just about every monitor has a HDMI port now. And if they don't a HDMI to DVI adapter they are about $5.
It's not just about connector choices, there's a limitation in the hw design. The 5000 products support a maximum of 2 legacy outputs. Legacy being DVI, HDMI, VGA, Component, whatever you like. So you can run DVI + DVI, or DVI + HDMI, or HDMI + HDMI, or VGA + DVI - any combination of two.
Most prior products are exactly the same - they support a max of two legacy outs.
On top of those two legacy outs, the 5xxx boards add DP ports. You can have as many DP ports as you like, up to the max outs supported by the chip (max is 6, for 58xx, I believe).
If you want to use one of those DP outs to drive a legacy monitor, you need an active dongle - i.e. a piece of h/w that interfaces with the graphics board as if it were a DP monitor, and then actively translates the DP content to drive a legacy display, generating all of the required clocks and signals, etc.
It doesn't have to be a $100 active dongle. It could be a $30 DP to VGA. Or some other design. But it does need to be active, because the board can only support two legacy displays, not three or five or eleven. Everything beyond those two is DP only.