Bring 5 cups water and the sugar to a boil in a heavy large saucepan. Stir until the sugar dissolves. Add the mint. Remove the pan from the heat and add the tea bags. Let the tea steep for 10 minutes. Cool the tea to room temperature. Strain the tea into a large pitcher or bowl.
Blend the watermelon and strawberries until smooth in a blender. Stir the fruit mixture into the tea. Add the lemon juice, peppermint and salt. Chill the tea until very cold, at least 2 hours and up to 1 day. Before serving, add chilled prosecco if using.
Put a few ice cubes into each of the 6 glasses or water goblets. Add some watermelon, strawberries and the blackberries to each glass. Pour tea into each glass and garnish with mint sprigs and serve, passing lemon wedges.