Fresh shell eggs can be stored in their cartons in the refrigerator for four to five weeks beyond the carton’s date with only a minor loss of quality. Once an egg begins to age, it loses moisture through its shell and begins to dry. The membranes that hold the egg structure begin to loosen and the yolk may not be anchored in the center of the white once the egg is broken. An older egg would be most appropriate for a mixed dish, a batter or a hard cooked egg which should be easier to peel than a freshly laid egg. But they're still safe to eat.