Not sure what you would expect - give her a cake with candles? Sing?
The usual answer is, they may or may not. The only guaranteed way to have something special on the table, or a birthday cake, is to arrange for it yourself.
If you haven't made a notation on your ADR that the dinner is for a 5 year old's birthday, try that. I would suggest getting her a birthday button at Guest Services. Have her wear it and see if she gets acknowledgements from the characters or staff when they see it.