Ok, wanted to give a followup.

I finally have the cards working together.  Now only one 7970 and two 5970s because the xfx 7970 decided to stop working .

I'm using only the newest drivers: http://support.amd.com/us/gpudownload/windows/Pages/radeonaiw_vista64.aspx. 

Catalyst 12.1 video drivers istalled fine for the 5970s, but the 7970 wasn't recognized.  Then I tried 12.8, which was a little better.  The 7970 was recognized, but wouldn't start.

The newest drivers worked for both 5970 and 7970.  The only issue that I have now is that the 7970 when running with the 5970s runs at a hash of 529KH/s, while running the 7970 by itself runs at 720KH/s.  I should mention that the setting are the same for the 7970 running with or without the 5970s.

I did have some trouble with cgminer not responding, so I downloaded Scrypt GUIMiner from https://bitcointalk.org/index.php?topic=150331.0 which runs them all just fine as long as I don't switch pools (my machine requires a restart for switching pools for some reason now).

Overall, not a great experience running them all on the same machine, but finally have them all working.  The 5970s are putting out at least 740KH/s each!