I'd probably start packing more food in his lunch box. Maybe divide it into 2 so he knows what is for what.
5 is about the age that both my children had a growth spurt that saw them eating pretty much the same as an adult some days.
I certainly pack more than that into DS1's lunchbox because he likes to eat a lot at school. DS is a lunch skipper so he has less and anything leftover is his afternoon snack unless his brother gets to it first.