Trying to do an un-bootable image disk backup on a re-formatted 1TB WD Passport external hard drive I am running macOS sierra on a mid 2012 MacBook Pro, and just recently came across a problem where I can no longer bypass login and got stuck on a loading screen before it eventually goes to a black screen and can no longer get into my Mac.

So, I decided to try and back up my stuff and migrate them to a new Mac I'm buying. I pop the WD Passport drive into the USB, go to the recovery mode and attempted to create a disk image backup from my MacIntosh HD onto it. But half-away, I am met with:

The operation couldn't be completed. (com.apple.diskutility error 3)
Preparing imaging engine...
Reading whole disk (apple_HFS : 0)...
Operation failed with status 5


I haven't got Time Machine activated, and I cannot even get into my Mac to use it. So I am left at a loss, trying to figure out how to create a backup.
If it fails on creating a disk image, then there may be one (damaged) file causing the problem.

Why not open the user folder and copy each sub-folder in turn and when you find the folder that fails copy the contents inside individually until you find the errant file... 

Of course, it may not be a personal file causing the issue...