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Combine 4 cups of granulated sugar, half and half and butter in a heavy pan.
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Cook over low heat, stirring gently.until sugar dissolves.
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Cover and cook over medium heat for 2-3 minutes to wash down sugar crystals from sides of pan.
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Sprinkle remaining 1 cup sugar in a heavy skillet.cook over medium heat, stirring constantly, until sugar melts and turn light golden brown.
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Pour caramelized sugar and milk into fudge mixture.
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MIXTURE WILL LUMP BUT WILL BECOME SMOOTH WITH FURTHER COOKING.
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Cook over low heat, stirring constantly, without stirring, until mixture reaches soft ball stage, 240*,
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Cool down to 160*.add marshmallows and vanilla.
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Beat with a spoon until marshmallows melt and mixture begins to thicken.
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Stir in black walnuts, pour into a buttered 9" square pan., spreading with a spatula.
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Cool and cut into squares.