Linden Lab says, in their system requirements, that some cards may not work, though most of them will work. Even the Intel Extreme Graphic that they say is incompatible also work [with a poor performance obviously].
Recently they updated the system requirements in the web page adding the ATI 5000 series, however when logging into Second Life with an ATI 5870 the viewer still do not recognise it, saying you have an incompatible card. Nonetheless It works! You should have no problems with either 5770 or 5750.