1. Cut and discard pits and peel from mangoes. Cut fruit into chunks.
2. In a blender or food processor, in batches, whirl the mangoes, orange juice, mint leaves, and 5 cups water until smoothly puréed; pour into a pitcher. Stir in 1/4 cup lemon juice, or to taste.
3. Pour agua fresca into ice-filled glasses. Garnish with mint sprigs.