Preheat oven to 350°. On a large baking sheet, melt the butter in the oil. Spread to coat the pan evenly and sprinkle with 3 tablespoons of the sugar. Cover with the banana slices in a slightly overlapping layer and sprinkle with the remaining 2 tablespoons sugar, the cinnamon and the peanuts. Bake for about 20 minutes, or until the slices around the edges are crisp and golden. Let cool slightly so they firm up. Transfer the browned slices to a plate and bake the rest for about 3 minutes, or until browned.