I wouldn't do it just because I hate getting up in the morning at 7am, so I know I couldn't do 5am ever!
I would definitely think about it because you don't want to agree to one thing, and then in a few months or so they change and ask for more earlier start days. Then you would start to feel obligated to say yes as you are already doing some for them. Start off with "special" they always think they are entitled to "special".