Place the seedless watermelon chunks in the blender and blend until smooth. (You may need to do this in multiple batches depending on the size of your blender.)
Pour watermelon juice through a mesh strainer and discard the pulp.
Measure out 5 cups of strained watermelon juice and add it to the blender with the frozen limeade. After it's blended well, serve ice cold with additional watermelon chunks.
Notes
Seedless watermelons really are necessary unless you feel like picking out every seed before blending!
The bigger the blender, the faster this process goes!
Feel free to use the can of frozen lemonade instead of limeade if that's more your style!
If you want to make this more like a slushy, freeze the watermelon juice into ice cubes, then blend with the limeade.
If you want to make this an adult beverage, add 1/2-2/3 cup tequila!