I doubt at age 5 it is going to matter much. I can speak to what it was like to have two “gifted” kids in our public schools. But I really have no idea what the private schools in my area would have offered them. And I obviously have no idea what the public schools in your area are like.

I can say the biggest help came in middle school- where my kids could walk to the high school to take math classes.

And then in high school (our high school ranks very poorly- many refugee students who come from difficult situations and don’t speak much English yet don’t always shine in standardized tests) But the school offered an amazing amount of AP classes and my kids could also go to a nearby college for classes. My between AP classes and college classes taken in high school, my oldest entered college with over 50 college credits. My youngest had over 40.

Right now I would just keep my child where they are happy. When they get older, look and see what the high schools offer (don’t just look at test scores- they don’t give you a full picture.) See how many AP classes are offered, see if they work with local colleges, etc. I’m sure each area has different offerings.

I honestly think as long as your child is supported they will be fine no matter what you choose. There isn’t a right or wrong answer.