If you follow the official recommendations of Apple, on very close reading, they say for three displays on a 5770 or 5870 that require adapters:
1) Use only ACTIVE (powered) adapters.
2) The only ACTIVE (powered) adapter Apple sells is the US$100 Dual-Link DVI adapter.
3) if you want genuine Apple adapters, that is the one you must buy.
ATI/AMD, the maker of the card says they have tested and approved a whole raft of adapters, including some that are ACTIVE Mini DsiplayPort to Single-Link DVI (works for up to 1920 wide or 1080p) in this article:
In the US, several of these are available for less at Amazon.
Read Carefully!! It MUST say ACTIVE or it is not. It must be Mini DisplayPort or it will not fit.
In the US, for displays up to 1920 wide, this third-party AMD gold certified ACTIVE adapter is available at Amazon for under US$35;
Accell B087B-006B UltraAV Mini DisplayPort to DVI-D Single-Link Active Adapter ATI Certified (Black)
And for displays wider than 1920 wide, this third-party AMD gold certified ACTIVE adapter is available for under US$90:
StarTech adapters that will do this job are also available.