I only recommend coolers that I already own. The zalman VF900 and the Vf1000 are just right for this card and are silent. They are somewhat expensive but they are solid copper unlike most coolers these days which are getting to be rare. Any thing else I am just going to say good luck.
It is worth a shot but if nothing improves then RMA your card beyond that there really isn't much that I can do to help aside from giving some advice. You can try cleaning your card or replacing the cooler.
because before when i did not change card i didnt have this problem, but efter i changed card its started to restarts and shutting down, and i also looking in to a program called CPUID Hardware Monitor it says my GPU temperatures is 44 celsius when im not playing games and when i play games its says 68 celsius. can this be something you think ?
assuming the power supply is working fine, you have plenty of power. is the issue only when skype is in use? it could be a software issue . also make sure the 6-pin power connector is firmly attached to your ATI 5770 and all Nvidia drivers from your GT240 have been uninstalled.
2) Download your new driver to the same place.
3) In add/remove programs, uninstall any Nvidia or ATI vga drivers and programs.
4) Boot into safe mode. Press F8 repeatedly while booting to enter safe mode. Your display resolution may be minimal.
5) Run driversweeper. Check the selection boxes for the removal of all nvidia vga drivers and ati drivers.
6) Rerun driversweeper. All such components should be gone.
7) Install the new driver from the desktop or saved location.
To verify that cooling is not an issue, open the side of the case, and direct a house fan at the innards. As others have said, graphics cards are built to run hot, and they do.