Crossfire 5770 with 7770

It's impossible. And if you tried, you would just not be able to enable it in Catalyst Control Center.

If you were able to crossfire them together, you would have to use the 5770 card as the primary card and the 7770 as the secondary because the second card is always downgraded to the same spec as the primary card.
In any case, the nm values have to be the same on both cards and your mobo must be Crossfire ready.