Is charging the iPhone 5s over night bad for the battery?
It shouldn't be a problem. Only time will tell but the newer batteries do have a better lifespan then say the iPod touch fourth gen that had a terrible battery lifespan/longevity and lasts maybe 20 minutes without dying if uv had it for 3 yrs
The new batteries are bigger and made differently so they can continue to hold their charge at about 80% in three or more years from now( or at least that is what apple claims) so the my final answer is
no you shouldn't have a problem
But do remember that leaving any rechargeable device plugged in for too long will minimize its lifespan ( as long as it isn't left in for more than 24 hours and you constantly keep it charging for long periods of time like 24 hours)