Can a novice user help to find a bug? I found that my Nexus 5 suddenly rebooted itself. I'm not a programmer so is it possible to set my phone such that it sends automatically sufficient information to the developers why it rebooted itself?
As @Izzy said, Android logs don't persist after a reboot.  So the answer is no.  Especially if your phone is crashing and not going through a proper shutdown.

One (hacky) solution would be to run ADB on your desktop and run logcat in a command window.  After your phone reboots simply cut/paste everything into a file and send it whomever you wish.  This will probably be the easiest solution for you.

The best (or easiest) solution will be to connect to your tablet with ADB adb shell and then run while [1]; do logcat &gt;&gt; /sdcard/logcatData.txt  done;
This will write all logcat data to a file under /sdcard/logcatData.txt and it will be there even after reboot.  You can then pull that file off the tablet after it's rebooted and send it to developers.

It will require ADB to be installed and minor command line use but it shouldn't be overly complicated.