I live in North Dakota and want to take my daughter to Florida for a week vacation. Her father is in prison and I haven't seen or spoken to him in about 5 years. Do I need to get his permission to take her on a plane to Florida for a week?

I assume you have legal custody ?

No, there is no permission needed to take your own child on vacation, if it is your time to have child and there is no restriction in a custody agreement. The time out of state can not be a move, and cannot interfere with other parents visits ( which does not from prison)

You should not. Especially if you have primary custody

Do you have custody papers filed with the courts? If so then consult them as to what you need to do. Some have it that you must notify the other parent and if things happened after the custody was decided and never changed you may have to let him know.