To the extent there was a contract (as opposed to an offer), it was for 5 nights. There was never a contract for 4 nights, so the hotel didn't change the rate on that contract.
The customer assumed that the rate wouldn't change, and maybe it wasn't communicated clearly (although every reservation I've seen always says something about early departures may result in changes). But that's a customer service issue- not a legal issue in the guise of a contract. If you had a rate you negotiated to buy 1000 widgets at $10 a piece, you couldn't send back 999 and insist you only owed $10 and not a dime more, as the price was negotiated based on the quantity. There was no contract for 1 widget, and thus the default price would be the market price.