Um, no five year old needs TWO private lessons per week.
It sounds like, unfortunately, you've found a money-grabbing coach.
While I do generally agree with this, and suspect the coach might be digging, I think it also very much depends on the situation. One of the women I grew up with was elite-track, she had all kinds of potential. It was evident early on (she trained with, and consistently beat the Weisses), and she was in
relatively hard core training by the time we were 6. Unfortunately for her, life events forced her to quit just as she hit Novice and things started getting interesting. A few other kids I trained with were also elite track and in hard core training from pretty young (all were Pam Gregory's students and went to Delaware with her when she moved). They were ultimately medal contenders at Nationals and competed internationally.
I agree with SarahSpins and TwokidsSkateMom- if groups are more productive than publics, I'd go that route, there's always time. If your daughter's showing elite potential, and you think she'd benefit from, and you can afford 2 privates a week, shoot, why not. Your daughter certainly loves it enough and will likely be happy whatever you decide. Make the decision that's right for your family.