I'm experimenting with connecting my guitar to my Nexus 5, how can I capture the audio signals from my guitar pickups through the 1/4" audio cable connecting my guitar to the 3.5mm audio jack?
You need an adapter that will convert the signal coming from the guitar to the signal used by your phone.
One such device is made by Peavy:
It claims to be for iPod Touch and iPhone but the jack is standard and the same on Android phones including your Nexus 5.