i got my 5770 up to 1040mhz Core, 1340mhz Mem. alot of it depends on your specific card and also your case cooling and setup. what brand of 5770 do you have?
to overclocking it CCC will work, but if you want higher speeds then i recommend Msi Afterburnerhttp://event.msi.com/vga/afterburner/download.htm
as for the Fan i have mine at full 100%, but thats because i have such a high overclock.
use furmark (and/or if you have a very GPU demanding game) to test your GPU temps. as long as you stay under 85C your ok.http://downloads.guru3d.com/FurMark-v1.6.5-download-1965.html
right off the bat dont try to get it as high as mine, increase 5-10mhz at a time, then after a bit try furmark to see if its stable.