This is soooo awkward! I had the same problem with my daughter on her 5th birthday.
We did invite everyone in the class but only for her first year at school. By the second year, little friendships had formed and it became easier to decide who to ask.
I like the idea of handing out invitations to parents though.
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5th Birthday Party by: Mary-Lou
This can be a difficult one....That's a lot of kids to be running around, let alone to cater for. If you can have the party in a park, then there's obviously more room and you can ask parents to stay and help.
At some stage though children need to realise that they won't be invited to every party (a harsh reality to some at first). When my own son had his 5th birthday party, I handed the invitations out directly to the parents once the children had gone into class. This avoided those little ones standing and waiting for their invite - who weren't invited.