Extract full system image from a Samsung Galaxy S5 with no screen I have a Samsung Galaxy S5 phone with a broken screen. I'm trying to get a full system image that I can then flash into a brand new Samsung Galaxy S5. 

I know that it is possible to clone one phone's system and configuration into another phone (e.g. using the procedure described here). However, that process assumes a fully working source phone.

How could I extract a functioning, flashable system image from a phone with no screen?

FYI: the source phone has USB debugging enabled, so it is possible to access it through adb.
If the source phone is rooted you have multiple possibilities. 
If the target phone is also rooted one easy solution may be a back as it is described in Is there a way to do Nandroid backup directly to pc and then restore it directly from pc also?

First connect via adb shell to the phone and get root permissions via su.

Now create backup all app files via tar:

tar -cvf /sdcard/app-data.tar /data/data


Then exit adb and copy the created file to your computer:

adb pull /sdcard/app-data.tar


Afterwards you should have a file named app-data.tar on your computer. Check it with an archive tool and you will find a lot of directories.

You may want to delete certain files or directories from the tar file.
Afterwards you can convert it to an Android Backup so that you can write back the data onto the new un-rooted phone. 
Making a tar file to an Android Backup can be done via Android Backup Extractor. Note that some apps will refuse to accept the restored files (because backup is disabled).

The created Android backup can then be restored via adb backup command.