You can certainly have 5 children in your home. Cupcakes and simple games - cheap and friendly and personal.
Or, if you are determined to have it at Chuck E. Cheese, you address the invitation TO THE CHILD and say "drop off at 1 PM, pick up at 3 PM". When the child is dropped off, you say, "Thanks so much for bringing her. We'll see you at 3!" Have a party table set for 6 kids - your daughter and the 5 guests. I'd be shocked if parents didn't figure it out. You do not have to specify that others are NOT invited - you simply invite those who are. If they make assumptions, they are wrong. Don't explain, don't elaborate, don't un-invite - just say "I'm so happy to have a small party so the kids can really interact and enjoy themselves." Resist, resist, resist the pressure to have a party of 20 kids! It's unnecessary, hectic, over-stimulating, expensive, and pointless. Your child will enjoy herself so much more if she only has a few kids. We always followed the "year rule" - if you're 5, you invite 5 kids. If you're 7, you invite 7. By 9, they want to go to the movies and you go back to inviting 3 kids who will fit in your car.
If anyone says "where's the chair for my 3 year old?" just act dumbfounded and say, "I don't understand." Pause. Pause again. Say, "Oh my, did you think this was a party for a bigger age group? I thought we were clear in inviting just kids in my daughter's class. I think it's so much more fun that way, don't you? Go enjoy yourselves and we'll see you in a few hours."