iPhone 5 backup fails, both to iTunes and to iCloud, no 'zombie' apps found
For anyone who happens to have the same problem: It turns out the database of the Whatsapp application seems to have been corrupted in some fashion. In order to see a live log for your iDevice, connect it to your Mac and open XCode. Under Window->Devices, there is a panel at the very bottom. When trying to backup unsuccessfully with iTunes, there where a lot of error messages, one of which read

&lt;Warning&gt;: ERROR: Backup error - open_dprotected_np error: Operation not permitted (1) at path "/var/mobile/Containers/Shared/AppGroup/BAB2BCE4-C114-410B-ABFE-8C6B140B9446/Library/Preferences/group.net.whatsapp.WhatsApp.shared.plist.YvjyOTy


I went ahead and uninstalled Whatsapp from the iPhone. After that, both iTunes and iCloud backups worked again.