DS2 did the exact same thing - not easy to look after a five year old on little or no sleep. I did the cruel to be kind approach - he was only a couple of weeks old - kept him awake as much as possible through the day, took a couple of days and he was in my routine (not me in his). He still woke for night feeds, but wouldn't stay awake half the night. Can make you feel nasty - but in the end it's worth it for your sanity.

Good luck