Right on. I didn't reference his state and only mentioned a possible approach for OP. You know, give a man a fish, or teach him to fish?
Three years came up because even if his kid was in kindergarten, which is not mandatory in all states, he might not be able to use school attendance as a means for the status quo for the school. Three years was an arbitrary number to provide an example.
If his kiddo has been in the same school for the last four years, then that would be a great approach to contest a move away from the mother. The kiddo would have established roots in that community. The kiddo would have friendships, activities, and such that could be a detriment to leave. Differently states, that it would not be in the child's best interest to be uprooted.
And, before you parse out that argument, yes, the mother is free to make her case based on best interest standards, as well.
But, with a five-year-old, that argument is a little more challenging. Does a five-year-old make that strong of friendships with classmates? That would require the opinion of an expert, perhaps. Can one contest a move away based on a five-year-old best friend?
I'm glad that you found the law for his state. That is helpful.
I am encouraging OP not to focus on just one thing to make his case; instead, he should find many details to bolster his case.
And, even more generally, for him, and any other poster, to look up as much information for themselves as possible.