In a saucepan over medium heat, stir together the water and sugar. Simmer until sugar has melted completely. Remove from heat and set aside to cool.
Wash the lime gently under water and dry. In a large pitcher, pour in the cooled sugar syrup, 5 lime wedges and muddle gently to crush the fruit but not release too much of the oils from the skin. Add ice and cachaca, and stir. Serve in a large glass garnished with a lime wedge.