1). The WindowsImageBackup folder is where Windows stores the backup of your system (or whatever you have chosen to backup).
2). A 22.7GB file does not compress down to 5.59GB, so I would have to ask exactly what your 5.59GB file is a backup of.
i did a screenshot to make things easier, http://puu.sh/21qNz
the SHAUN-PC is the 5.59GB (obv ignore Steam file) then last one, WindowsImageBackup is 22.7GB and looks like this inside the folder: http://puu.sh/21qPL
then inside the BackUp file i have this http://puu.sh/21qQq
i was thinking maybe the SHAUN-PC 5.59GB file uses the WindowsImageBackup to help restore but i'm not sure