I have LR5 on a mac mini (OSX 10.10.5) that recently started telling me "Lightroom was unable to back up the catalog named "Lightroom 5 Catalog" when closing. Prior to this, I had no problems with automatic backup of catalogs after closing LR and can't recall any changes that would have prompted this. I already checked the folder permissions (read & write for all users), tried choosing a new backup folder (didn't work), and checked available space on my hard drive (>300 GB available). Any suggestions? I am looking forward to upgrading to LR CC, but want to get this resolved first and have a good backup of my catalog.
Are you backing up to the internal hard drive or an external had drive?
What is the exact error message you are getting?
Have you tried to create a new folder and or save other files to this drive, even just a text file, and what happens, Error, No Error file saves or folder can be created?
It is more than likely a Folder permissions problem. Select the option to Choose a Different folder to backup to. Try one in your Home, Username, folder.