Should they take no action the transfer will be automatically approved on the fifth day. The registrar simply should check to see that your account has been paid in full, and if so, approve the transfer. All the registrars seem to be good about doing this. The transfer will be completed and you can manage your domain from our systems. Through this whole process you can login to our system and see exactly what step your domain transfer is in.
Domain transfers involve the participation of a number of parties.
They can happen as quickly as a couple days or take as long as two weeks. It's just the law of the land. The current admin contact's e-mail address must be able to confirm the transfer request. If the administrative e-mail address on the domain registration is incorrect, you need to first fix that with the losing registrar before attempting a transfer. This condition can exist for many reasons including lack of payment or domain expiry.