I've used AMD overdrive to OC my 5770 and I must say that the auto overclocking feature plain sucks. Even after it has tested the overclock that it recommends, I see frequent game crashes and "The display driver
stopped responding" errors.
I find MSI Afterburner to be WAY WAY better than AMD Overdrive in terms of OC'ing. You can log your temperatures and find out exactly how hot your PC runs when you're gaming, set custom fan profiles to keep your GPU at temps that you think are acceptable. And if you're planning on going a little further, a little .ini tweak allows you to change voltages and unlocks OC'ing abilities to allow you to push your card even further (I would recommend NOT to meddle with these things if you do not know what you're doing. You could end up SERIOUSLY damaging your hardware).
My recommendation would be to install MSI Afterburner, and use GPUTool to stress test your card. Increase the core clock first in increments of 10Mhz and stress test your card with GPUTool for 1 minute after each increase, till your card gives you a "Display driver has stopped working" error, or till it shows other signs of instability such as artifacts in GPUTool. Then decrease the core clock by 5Mhz till the card is stable again (Run GPUTool for a few minutes this time). This will give you your stable core clock OC. Then do the same with the memory clock (with core clock reset to normal while you do it). When you've found the maximum core and memory clocks and want to apply them, you may have to reduce one or both of them slightly to get your card stable.
This is what I do. Hope I helped.