I've had the endless boot animation problem before, it's hard to tell if an application's data is causing the issue, or an app itself. I don't believe there's a way to boot into Safe Mode from bootloader. I'm afraid your arguably easiest fix is to factory reset it and configure it again.
Sometimes when a Nexus is stuck in bootloop, I'll hold the POWER button down until the screen goes blank again, and without releasing the POWER button, hold VOL DOWN.[1] That may get you into bootloader. From there enter Recovery, and in Recovery you can factory reset it. It should boot normally and then take you through setup.
[1] Google's information for the Nexus 5 states that bootloader is reached with both VOL UP and VOL DOWN along with POWER, but my refurbished unit works with only VOL DOWN and POWER.