Max, all a day of rest mean is a pitcher didn't pitch on a particular day. E.g., Pitcher A pitches a game on a Sunday. With no off days in the teams schedule, his next scheduled would be Friday (with Mon, Tue, Wed and Thu counting as days of rest). Another way of putting it is he pitches every 5th day (which is what your 5-6 day calculation is telling you).
Back in the day, teams had 4 man rotations and pitchers used to go every 4th day, meaning 3 days of rest between starts. That's how they used to start about 40 games a year. With modern 5 man rotations, it bumps up one.