Preheat oven to 325 degrees. Spray baking sheet with nonstick spray. Combine corn syrup, sugar, salt, pepper and cayenne pepper in bowl. Stir to blend. Add nuts; gently stir to coat. Transfer to baking sheet.
Bake nuts for 5 minutes. Using fork, stir nuts to coat with melted spice mixture. Continue baking until nuts are golden and coating bubbles, about 10 minutes. Transfer to a piece of foil on work surface. Working quickly, separate nuts with fork. Cool. (Can be made 3 days ahead. Store airtight at room temperature.)