Place the almonds, cashews, pecans, walnuts and pistachios on a parchment-lined baking sheet. Transfer to the oven and toast until golden, 10 to 15 minutes.
Meanwhile, mix the brown sugar, salt and cayenne in a small bowl and set aside.
Combine the honey, corn syrup and vegetable oil in a small saucepan. Bring to a boil, then pour the hot mixture over the toasted nuts, tossing to coat evenly. Stir in the brown sugar mixture, then spread out the nuts on the parchment and let cool.
Once cooled, break into pieces. Store in an airtight container.