BSOD crashes after updating/reinstalling Radeon HD 5670

   Warning

Before changing any drivers, make sure that you have earlier System restore points made in your computer. You can check it easily by using CCleaner looking at Tools > System Restore.

If there is no points, make a System Restore Point Manually.

Avast can cause some issues.
Please remove it and replace it with MSE and Malwarebytes.

   Warning

Make sure you don't enable the free trial of malwarebytes pro

You also appear to have an Atheros Extensible Wireless LAN device driver installed but I can't see a component for it in your msinfo32 file.
Can you remove it completely.

Remove your Realtek Ethernet controller driver as well as there is no timestamp on it.
Download it again here.

Realtek

Can you also remove the CD-ROM Class Filter Driver by Gear Software for testing purposes.
It actually comes with iTunes so you would have to use that.
I suppose we can leave it for now if iTunes is important to you.

Post back the results.

I think I was able to accomplish all suggestions with the exception of the Realtek driver. I followed the link you provided but am unsure of where to go from there. I also have a question that seems silly to me but I'd rather ask and know the answer. When I download the current AMD driver, install, etc., then go to Device Manager>Display Adapters>ATI Radeon HD 5670>Driver, it still lists the older version and original date from 2009. Is that normal? Should it not show the updated driver version and date downloaded?

It is a desktop.

Using the AMD Catalyst Install Manager isn't doing the job so I'm guessing I need to additionally go into system files to manually delete old drivers. (I've tried the AMD Driver Autodetect Utility to no avail; it won't run). Do you have suggestions to guide me in this manual process? Some of the old drivers are ATI and some are AMD. These are the ones I see in OS:

amdacpksd.sys
amdide.sys
amdk8.sys
amdppm.sys
amdsata.sys
amdxata.sys
ati2erec.dll
AtiHdmi.sys
AtihdW76.sys
atikmdag.sys
atikmdag.sys.old
atikmpag.sys
atipmdag.sys

Also, I did remove Avast and replaced it with your suggestions.

Thank you!

You don't manually delete drivers, you have to remove the entire software package, try using Revo Uninstaller to software that can cling to your computer. Use Advanced Mode to remove leftover registry entries:

Download Revo Uninstaller Freeware - Free and Full Download - Uninstall software, remove programs, solve uninstall problems