Wash whole watermelon and cut watermelon in half. Use a large spoon to scoop out all of the pink part of the watermelon into a bowl. Discard or save watermelon rind for other use (pickled watermelon!).
Puree watermelon in blender. Measure how many cups of watermelon puree you have. A 5-pound watermelon will yield approximately 8 cups of watermelon puree.
For each cup of watermelon puree, add ¼ cup of water and 1 tablespoon of lime juice. For example, for 8 cups of watermelon puree, add 2 cups of water and ½ cup lime juice.
Stir everything together in a large pitcher. Taste. If you'd like, stir in sweetener, though if you're getting good watermelons, you probably don't need any sweetener.
Watermelon Agua Fresca is ready to drink, but Watermelon Agua Fresca is even better once it's chilled in the refrigerator for a couple of hours. Stir again right before serving (watermelon pulp might settle toward the bottom).
Pour Watermelon Agua Fresca into glasses, over ice if necessary. Garnish with lime wedges and/or mint sprigs.
Watermelon Agua Fresca will keep in the refrigerator for about two days.