In a 2-gallon bowl, pitcher, or other container stir together the lemonade concentrate, limeade concentrate, cranberry juice, water, and rum. Cover and chill up to 48 hours before serving.
To serve, transfer the juice mixture to pint canning jars or a punch bowl. Float lime slices in punch. Serve well chilled or over ice. Makes 52 (1/2-cup) servings.