If you searched the web and learned a lot of people had the same issue, you should have probably learned the solution, too.
In case you don't know the solution, raising the idle (2D) core/memory clocks by a little margin resolves the issue. This is done through creating a profile and changing the idle clocks.
I have the same chipset card (HD5770). I had that problem before and resolved the issue by increasing the 2D (idle) clocks from 157/300 to 200/400. This continued till CCC 10.5 was released. After installing CCC 10.5, the problem never happened and I abandoned the profile method. I cannot say if it is CCC 10.5 that actually resolved the issue or a Windows update that I had. I now have CCC 10.6. It also seems O.K. till now. But this CCC version is too new (I installed it on June 17), therefore, I cannot comment. By the way, I have Win 7x64.
The theory that lies under the profile method is that the idle (2D) clock speeds are set by AMD too low to maintain stability. Increasing them brings stability.
The profile method is outlined here (copied over from the internet):
1. Open CCC
2. Unlock and Enable Overdrive if they aren’t already.
3. Go to Options/Profiles/Profiles Manager. Create a new profile. Give it any name you want. Under composition make sure “ATI Overdrive” is checked. Save and Close, DO NOT ACTIVATE THE PROFILE YET.
4. In windows go to: C:\Users\{yourusername}\AppData\Local\ATI\ACE\Profiles (you will need to have “show hidden files” turned on for you to see this directory)
5. Open the .xml document with the name of the profile you just created (notepad is fine)
6. Change the values of the Core and Memory speeds to look like this (these specific values are what worked for my card from other manufacturer, increase them in small increments if they do not work for your card) EDIT ONLY THE BOLD VALUES.
Feature name="CoreClockTarget_0"
Property name="Want_0" value="20000" (previously 15700)
Property name="Want_1" value="60000"
Property name="Want_2" value="85000"
Feature name="MemoryClockTarget_0"
Property name="Want_0" value="40000" (previously 30000)
Property name="Want_1" value="120000"
Property name="Want_2" value="120000"
7. Save and close. Go back to CCC and activate the profile you just created.
This will make the card idle at 200 core clock and 400 memory clock. (2D clocks are the "Want_0" values). You can see the new speeds on the Overdrive page of the CCC.
But I suggest you try CCC 10.5 or CCC 10.6 first. If it does not resolve the issue, you then try the profile method.
Hope this helps.