In a small saucepan over medium heat, combine 1 cup of water with the sugar. Stir until sugar has dissolved to create a simple syrup, then remove from heat.
In a blender, combine strawberries, basil leaves, and the simple syrup. Blend until smooth.
Pour the mixture through a fine-mesh sieve into a pitcher to remove pulp and basil solids.
Add fresh lemon juice and the remaining 5 cups of water into the pitcher and stir well.
Serve over ice and garnish with fresh strawberry slices or basil leaves if desired.