They will crossfire, the overall result will likely be slower than a single 5870 though.
Crossfire is asynchronous but there is a lot of overhead. In time gone by the result woudl be identical to 5770 crossfire... but now a days there is an improvement with roughly close matching cards (at least in the 5000 series). You might see something a touch faster than a 5870 but the overhead woudl be large and who really knows how well ti would work. Best case is something nicely between a 5870 and 5850 crossfire.