Download and Install Photoshop CS5
As per the comment from user3439894 the issue was that I had 


  System Preferences > Security &amp; Privacy > General > Allow apps
  downloaded from:


set to


  Mac App Store and identified developers


Once I set it to be


  Anywhere


Then I could run the installer.  

The error message I received was disingenuous and did not inform me of what the actual problem was.



Protip - Even though Adobe wouldn't tell me what my CS5 license number was there are ways to extract it from OS X.  It just took some googling.