Combine sugar, 1 cup water, and 5 mint sprigs in a small saucepan. Bring to a boil over medium-high, stirring until sugar is dissolved. Remove from heat, and cool completely (about 30 minutes). Discard mint sprigs.
Process 6 cups chopped cantaloupe and 1/2 cup water in a blender until smooth, about 1 minute, stopping to scrape down sides as needed. Pour mixture through a fine wire-mesh strainer into a pitcher, discarding solids.
Stir in mint syrup, lemon juice, 2 cups cold water, tequila, and 5 mint sprigs. Chill until very cold, about 4 hours. Serve over ice, and garnish, if desired.