Combine 1 cup water, sugar, and ginger in a small saucepan; bring to a boil, and cook 1 minute or until sugar dissolves, stirring occasionally. Remove from heat; cool.
Strain ginger mixture through a sieve into a pitcher, and discard solids. Add 5 cups water and juices, and stir well. Serve over ice, and garnish with lemon and lime slices, if desired.