[Q] Nexus 5 stuck at screen of the eternally spinning balls

I'm going to start off by saying I'm the noobiest of noobs, so please be gentle with your replies.

I was watching Youtube on my Nexus 5 yesterday when it suddenly shut down and attempted to restart itself. I watched it go very slowly from the white Google logo to the colourful spinning balls screen, and it got stuck there.

Status right now:

• Phone stuck at spinning balls screen


• I can get to fastboot and factory recovery screen


• Factory reset doesn't work


• Power button appears to be working fine


• Charging is fine and I can see the battery icon when it's off


• Phone is not rooted, bootloader has not been unlocked

What I did so far:
Someone posted a thread with a similar problem and said to flash the factory image a few times, so I followed these instructions. Except to do that I need to unlock my (currently locked) bootloader first. I then tried to follow these instructions of unlocking bootloader, but got stuck at the last step of "fastboot reboot“ because my phone still won't get past the screen of spinning balls, no unlocking the bootloader for me. HELP!

This is what's at the bottom of the system recovery screen:
E: failed to mount /cache (Invalid argument)
E: Can't mount /cache/recovery/log
E: Can't open /cache/recovery/log
E: failed to mount /cache (Invalid argument)
E: Can't mount /cache/recovery/last_log
E: Can't open /cache/recovery/last_log
E: failed to mount /cache (Invalid argument)
E: Can't mount /cache/recovery/last_install
E: Can't open /cache/recovery/last_install
E: failed to mount / cache (Invalid argument)
E: Can't mount /cache/recovery/last_kmsg
E: Can't open /cache/recovery/last_kmsg
E: failed to mount /cache (Invalid argument)