How to update OS X in single user mode?
Single user mode disables many of the system demons and processes needed to run an update.

Instead of that, I use the createistallmedia tool to make a bootable installer on a USB drive and I boot to that OS  that is exceptionally limited and controlled by Apple and exists only to run the installer.

The downside of this method is that you need apple to release an installer based on 10.10.5  and it's also a bit of chicken and egg problem if you start asking which operating system do you trust to create the installer in the first place. 

See https://support.apple.com/en-us/HT201260 for details on which build corresponds to which numbered release.