Some registrars will refund you if you cancel the name within 5 days of registration (the registrar gets the money back and extends the courtesy to you). After 5 days the registration becomes firm and no refund can be granted.
What I can't understand is if you are referring to the 4-5 days grace period (in which case you'll get a refund) or to the domain expiration.
If the case is the latter you'll simply lose the domain, and you won't get any refund.