I'm fairly certain you can't crossfire a 5870 and a 6970 as they are from different series, and infact use a slightly different architecture. Your best bet would be to just pick up another 5870 (I'm assuming this is what you have now?) and crossfire them together. 2 5870's is still more than enough to run everything very well.
Different architectures, I'm pretty sure you can't crossfire those like Yargnit says. Even if you could, I'm not sure you'd want to anyway. I'd also be tempted to just crossfire the 5870 and wait until the next series of cards. A 5870 can be bought for buttons these days.
If you mean 6-screen eyefinity you'll need an eyefinity 6 edition card. Is that what the game edition is?
Also if you want to run 6 screens you definitely want to get a 2gb card for the memory, or the 4gb 6990. I wouldn't recommend crossfiring the 5870 for 6 screens as the main bottleneck is the 1GB memory on it and having 2 cards won't make any difference to that.
But I am getting a pci-e 3.0 motherboard so both are going to run at x16 so they shouldn't bottle nick should they?
When it comes to screen resolution the most important thing is how much onboard memory is on each card. Even though a crossfired 5970 and 5870 would have tons of shader power, they would struggle to power 6 screens because they would simply run out of memory, or frame buffer. A lot of the shader power would be wasted because without the memory to hold the information on all 6 screens, the frame rate would just crash. This is also why Nvidia cards struggle at the top resolutions unless they have 3 Gb per card. Even 1.5 Gb per card isn't enough in some games at very high resolution.
With 6 screens you definitely need to get 2 Gb per card trust me.