They need to be within the same chip family. You can crossfire a 5850 with a 5870 or a 5970, but you cannot crossfire it with a 5770 or a 6850.
^Mostly true, but you also get degraded performance putting a faster card with a slower one. The only case it's generally a good idea would be a 5970 and a 5870 because the 5970 has almost identical internals to the 5870, so it works quite similar to tri-SLI 5870s...
But a 5870 and 6870? No. At least it shouldn't work.
Here is a link to the ATI Crossfire compatibility charts showing what works with what. Unfortunately AMD has not updated it yet to reflect the 6000 series. Very strange. But none of the listed combinations cross over a series - e. g. no 4000 series card can be CF with a 5000 series.
Even if it worked (which I don't think it will), they would lower themselves to the lowest denominator (ie: run like two 6870 (slowest of the 2)).
Thanks. I was going to pick up a 6870 until the 5870 was sold and then pick up another 6870.
Well you're not going to sell the 5870 for much anymore, so at best you'll spend a little more money on two 6870s for at best equal performance as the two 5870s. 5870s are better cards, but the 6870s have slightly better CF scaling so they end up pretty equal in CF. Ultimately tho if you want an actual upgrade go to 6950/6970 over the 5870.
Just going to pick up another 5870 and call it a day or year.