You can probably squeeze some 3-400mhz without raising voltage, so there will be no additional heat.
I`d you want to go more, you`ll be fine for some 0.05-0.1v increase. Then, you have to consider getting a better cooler.
Best bet is to install AMD Overdrive (
http://game.amd.com/us-en/drivers_overdrive.aspx) and overclock from desktop.
And don`t be afraid to overclock that graphics card. You`ll probably get more fps`s by doing that. 5770 is a cool little card with lots of overclocking headroom. Through ATI Control Center, you can probably get some 100mhz on the core and 200mhz on the memory without any worries. But go easy after that and monitor temperatures. Don`t go above 60C for the CPU and 90C for the GPU.