I think most performance ATI cards spin the fan at 100% upon initial boot. My 4890 does it too. Once it boots into the OS, the fan speed drops to just 27% at idle. It may be a protecting mechanism. I don't see how it's an issue though since I imagine it's much more inconvenient to keep shutting down your computer every night and then wait a minute for it to boot every day (unless you have an SSD). I prefer to keep my computer on 24/7. From reviews online, 5770 seems to be a quiet card as well. Did you try setting up a custom fan profile?
The problem is mainly when you boot into an OS that doesn't have a proper ATi driver.
If I boot FreeBSD or a linux live DVD, it will just keep spinning 100% all the time.
I think that's silly. Firstly, I don't think I've ever heard it spinning 100% during a game, so I doubt even in 3d-mode it would need 100% fan speed.
Secondly, why would it boot up in 3d-mode anyway? It should boot up in 2d-mode, with low GPU clocks and fan speed, so that it's not burning up your GPU for nothing.
If you have no proper driver loaded anyway, there's no way you can make use of decent acceleration, and as such you don't need the full GPU power anyway, and thus no need for full fan speed.
So boot it up in 2d-mode, everything nice and low, and let the driver switch it into performance mode when required.
ATi used to do it right with their older cards. I have an old 9600XT that's nice and quiet until you really use it.
I have an X1900XTX which goes 100% when it powers up, but immediately goes back down to idle (perhaps they just want to make sure that the fan speeds up that way).
Why did they change a good thing?