Add 5 cups seedless watermelon to blender and puree until very smooth. (You may need to work in batches.
Place a fine mesh sieve over a bowl or pitcher and strain pulp from juice through the sieve, pressing on the solids with the back of a spoon to yield the most juice. Discard solids.
Combine the juice, 3 tablespoons simple syrup and 4 tablespoons lime juice in a pitcher and refrigerate until very cold.
TO SERVE:
Pour watermelon water into a glass filled with ice and garnish with fresh lime wedges, mint leaves and a wedge of fresh watermelon for an eye-popping presentation.
Notes
Store in the refrigerator in a pitcher or jar with a tight fitting lid. Pulp can settle on the bottom, so it needs to be stirred or shaken before pouring a glass.