To make a simple syrup, combine sugar, salt and ½ cup water in a small pot. Bring to a boil. Stir, and reduce heat to medium high. Stir occasionally until sugar is dissolved, approximately 5 minutes.
Let the simple syrup cool.
Blend the raspberries with 1 cup of water and the lime juice.
Pass the mixture through a strainer into a pitcher.
Then add the remaining 5 cups of water and ¼ cup simple syrup to the pitcher.