All user accounts on iMac running OSX 10.10.5 vanished on login screen
Backup first, via a second Mac if possible:

If you have a second Mac, you can put the troublesome one in Target Disk Mode:


During startup, hold the "T" key.  
Connect the two devices with Thunderbolt cable, or Firewire
The Target Mode device should mount like an external disk on your second Mac.
Make your backup.    


After you have a backup (or choose not to make one)...

Try to create a new (admin) user:


Boot back into Single-User Mode (CMD-S) during startup.
Mount the drive: /sbin/mount -uw /
Remove this file: rm /var/db/.AppleSetupDone
Restart the computer: reboot 
Go through Setup Assistant


Once you have a new Admin user, see what you can do with the accounts.