yeah, it consistently is telling you that the fastboot flashing operations are failing ("FAILED..."), so the bootloader is not actually unlocked...It's also not a case of needing the "OEM Unlocking" set to enabled in the Settings -> Developer options menu since the Nexus 5 (hammerhead) does not have that option or restriction like many of the newer devices do.
Not sure where to have you go from here...we've seen this before on a few Nexus 5 and 7's, too, unfortunately...
(we might have to get this account merged with your other one if so...no biggie, just let us know).
. In other news, a friend of mine told me about a command called "fastboot flashing unlock" that unlocked his bootloader, would that apply in my case? Or is it time to say goodbye to my beloved phone