When my husband and I entered our lease my son was 2 years old, since that time he has turned 3. According to our lease 5 people can't live in a 2 bedroom apartment if 4 people are 3 and older. My children are 1,3, and 9. Will I have to move, or will I be able to renew my lease.

That rule is not a law and was likely made up by the owner. The only way you will know is to ask. They do not have to renew you even if it were just you and your spouse. A renewal is an agreement from both sides

Since you agreed to that provision in your lease, you are bound by it. Obviously you had to be aware that your son would get older. And, I suspect so was the landlord. You can talk to him and see what you can negotiate, but I'm suspecting he isn't going to renew.

More than likely this is a rule made by the county zoning department. Your landlord included this zoning department rule in your lease. The landlord really should not renew your lease as you will have to move out lease or no lease due to the county's rules. It's like that where I live as well even in a private home situation only so many individuals living in a home applies across the board - not just an apartment situation.