I'm slightly confused? Did she really mean "same age"? Based on what were shown in the chapters, I will say that's unlikely the case.
There are 2 possibilities.
Firstly, she was meaning it only counted when it passed their birthdays. More narrations would be needed if that's the way she counted their ages.
Secondly, it's highly possible that translator misunderstood the context. In this case they were born literally in different years. With the 5-month gap, Mizuha was born the year later. So the term here should be same school year or same grade.
So I went and checked the raw. The word is 同い年.
Detailed explanation is: [補説]学校で、同じ学年であることを指すこともある。
@Garysanderson96
Edit: it seems that Japan also adopts the full-year count system from the West. If so there's not any contradiction here. Move on.