yes you can crossfire different cards of the same model, heck you could even xfire your 5770 with a 5750 (not that you'd want to but its possible)
with amd they only have to be the same series and make sure your mobo supports crossfire, and that your psu can handle 2 5770's if yes then they should work fine
important note though is the clocks of the two cards will ahve to match so whichever has the lower clock speed the higherclock card will downclock to that card's speed