I've found that this problem lies in the Boot Camp 4 MSI package, which is called on by Boot Camp 5 to remove Boot Camp 4. The Boot Camp 4 package resides in the Windows Installer cache (c:\Windows\Installer). To solve this problem, you will need an MSI editor like InstEd or Orca. I used Orca. Orca needs to be installed before you try to edit the offending MSI package.
First, you will need to identify which MSI package in the Installer cache is the one for Boot Camp 4 by finding out which package Boot Camp 5's installer is calling for uninstallation. To do this, you will need to go into Boot Camp 5's Apple driver folder (Drivers\Apple) in File Explorer. From File Explorer's File menu, mouse over "Open Command Prompt" and select "Open Command Prompt as Administrator". This will start a Windows Command Prompt at the exact folder you need. Type in "BootCamp.msi /lx log.txt". This will run Boot Camp 5's installer and log extra debugging information to the file "log.txt". After that, you can close the command prompt window. In File Explorer, you should now see a file called "log" with a type of "Text Document". Double-click it to open it in Notepad, then Find (Ctrl-F) "c:\windows\installer" and keep hitting Next until it gets to the last location of it. That file name should be the Boot Camp 4 package in the Installer cache. Make a note of the name. On my system it was "420ef.msi", but yours may be different.
Next, open another File Explorer window and in the path bar above the file listings, type in "C:\Windows\Installer". You will most likely NOT be able to simply browse to it because this folder remains hidden for very good reason. Once you're at the Installer folder, type the name of the MSI package in the search box next to the path bar. This will narrow the selection down to this one file. Right click on it and select "Edit with Orca".
In Orca, locate the table "LaunchCondition" in the left-hand pane. Click on it, and you should see a number of rows of entries. One of these will likely say "VersionNT = 601" in the left column and the now-familiar "Boot Camp requires that your system is running Windows 7" in the right column. This is the offending entry in the LaunchCondition table. Double-click on the left column (where it says "VersionNT = 601") and change it to "VersionNT >= 601". (If you're running Windows 8, VersionNT has a value of 602.) Hit Enter to make sure the change sticks, then Save the MSI package and close Orca.
After that, go back to the Boot Camp 5 directory and run setup.exe. The installation process should then continue without interruption.