There are two conflicting units at work here. One is the ream as
mentioned in the question and one is the quire.
"Short" paper measurements insist that there are 24 sheets in a
quire and 20 quires in a ream, therefore, "short" paper
measurements give 480 sheets to a ream.
Writing paper measurements give 25 sheets to a quire and 20
quires, therefore, 500 sheets, to a ream.