The subtle charms of quinces are easily revealed. Naturally occurring pectin in the fruit lets preserves set without added thickeners.
Bring quinces, 1/2 cup sugar, and the water to a boil. Cover, reduce heat, and simmer gently until quinces are tender, about 1 1/2 hours. Transfer quinces to a plate to cool. Reserve cooking liquid.
Coarsely chop quinces, and return to pot (including seeds, cores, skins). Bring to a boil. Slowly stir in remaining 5 cups sugar and the lemon juice. Cook, stirring, until preserves are thick, orange, and register 220 degrees on a candy thermometer, about 25 minutes. Pass through a fine-mesh sieve; discard solids. Let cool.