How did you make your bookings and are you certain you have actually been charged for those nights?
I am doing the same thing, but was advised not to book through the Parador website directly. I was told to contact each Parador separately via email, make the reservations (letting them know I will be using the 5 night card), and they will not actually charge my card. I did have to provide credit card information, but it was clearly stated that it was to hold the reservation, not to purchase an evening in advance. Plus, by contacting the Parador directly, I am given the option of cancellation within 24 - 48 hours without fee. Not true if booking through the web site.
I think it all depends on how you booked. I would think that if you have pre-paid and pick up your 5 nights card at the first Parador, then the subsequent Paradors should reverse the charges on your credit card at check in. I would contact each Parador and confirm this, however. (Their emails are <<name>>@parador.es - example: toledo@parador.es)