Stock Nexus 5 reboots randomly
Find problem apps by rebooting to safe mode

If your device keeps restarting itself, freezing, crashing, or is slow to respond, it could be caused by an app you’ve installed. You can use safe mode to start up your device with only the original software and apps that came with your phone. If the issues with your device go away in safe mode, the problem is probably caused by a third-party app downloaded on your device.

Use safe mode to find problem apps


Make sure your device's screen is on, then press &amp; hold the Power
button. 
In the box that opens, touch &amp; hold Power off. 
You’ll see a    “Reboot to safe mode” box.
Touch OK. Your device will start up in    safe mode.
Try using your device normally. Remember, you won’t be    able to use
any installed apps.
If the problem goes away: Restart your device to exit safe mode.
Uninstall recently downloaded apps one by one to see if you can
find the app that’s causing issues.


If the problem still doesn't go away one more option


perform a factory reset