Combine potatoes and water in a Dutch oven; cover and cook 10 to 15 minutes or until potatoes are tender. Drain, reserving 5 cups potato liquid. Reserve potatoes for other uses.
Allow 1 cup potato liquid to cool to 120° to 130°. Combine flour, 2 tablespoons sugar, and yeast in a large bowl; stir in the 1 cup cooled potato liquid. Cover and let stand in a warm place (85°) for 4 hours. Stir in remaining 4 cups potato liquid and 1/2 cup sugar. Cover and let mixture stand in a warm place overnight.
Stir starter well; reserve 1 cup. Stir 2 tablespoons sugar into reserved 1 cup starter, and pour into an airtight 2-cup glass container. Store in refrigerator until ready to use for second batch of bread.
Use remaining 4 cups starter to make Foolproof Salt-Rising Bread.
Note: To make a second batch of bread, use reserved 1 cup starter plus 3 cups plain potato water to equal 4 cups starter.