So, I've decided the time has come to root my nexus 5, but as you might have noticed from some of my posts I don't have a computer (or easy access to one).

So, is there any way to do it without one?

Sadly if you want to root your Nexus 5 you will need a PC.

Look here: http://www.tfq.me/how-to-install-custom-rom-on-nexus-devices-without-computer/