Those are there because you deleted the recovery partition. When you boot to the recovery partition it creates several RAM disks in memory for cache files etc. With no recovery partition and a Internet recovery boot those cache files get created in the main drive and that is what you are seeing there with that disk 4 and 5 business. One for each of what would have been a RAM drive.
Okay... let's try again and this time delete the logical volume and the logical volume group both in that order.
Do another diskutil cs list command. Note the UUID for the logical volume at the bottom then run this using your real UUID. This will be the very last UUID (disk3).
Code:diskutil cs deleteVolume BABCE092-XXXXX
Okay, not let's do the delete for the logical volume group at the top like before. Again use the real UUID form the new diskutil cs list run.
Code:diskutil cs delete FB6D7F84-XXXXX
Now go back to Disk Util and do the fix business again.
I believe my error was the volume needs be killed before the volume group can be killed.
Afternoon WeaselBoy,
I have experience a very similar situation, I was wondering if you might be able to help me get through the last stage. All of the errors and steps above have mirrored my own HD issues. However once I got to this very step around deleting the volume first the result is not as successful. I still receive the contact apple care message.
Bit more on my particular issue, same iMac and HD, the OS that is trying to reinstall is OS X Mavericks
I was on Yosemite before the total failure.
Any advice would be greatly appreciated, been having a go at this for a couple of days now!