In a small pan, combine 1 ½ cups water with 1 cup sugar. Cook over a medium heat, stirring constantly, until the sugar dissolves. Turn off the heat and drop in 1 sprig of rosemary. Set aside to cool. Once cool, remove the rosemary sprig.
Juice the lemons. In a large pitcher, combine the lemon juice, sugar water, and remaining 4 ½ cups water. Stir together. Serve over ice, garnished with a few lemon slices, and the remaining rosemary sprigs.