Does cracked screen cause faster battery drain? I dropped my Nexus 5 a week ago and the screen cracked diagonally 8cm from side to side.

Since then I am sure that the battery drains faster than before. Previously I was always happy at how much battery life was left during the day, based on my experience of Nexus One and Galaxy Nexus. Now I am always noticing how quickly it is going down.

I didn't measure battery usage before the damage so I can't prove my suspicion. The battery usage settings screen shows the screen as the highest battery user, as before. Again, I'm sure the recorded percentage of screen battery use is higher than previously, but I don't have figures from before the break.

So, could there be a reason for the screen to use the battery more when it is cracked in half?
It could be that the visible crack isn't the only damage to your phone. If a connector is shorting in the screen or another component, that could be draining the battery (as well as generating heat).

A short could also cause sparking around the damaged component, which will cause further damage over time. You should get your phone repaired. If you tell the mechanic that you broke the screen by dropping it, they'll know to look out for other damage while they disassemble the device.