Crush enough cookies to make 1 3/4 cups crumbs. In a 9-inch cheesecake pan with removable rim, mix cookie crumbs, granulated sugar, and butter. Press over bottom and about 1 inch up pan sides.
Bake crust in a 325° oven until slightly browner, about 15 minutes.
Meanwhile, in a food processor or in a bowl with a mixer, blend cheese, brown sugar, and eggs until smooth. Spoon 1/2 cup of the cheese mixture into a small bowl. Add five spice and pumpkin to remaining cheese mixture and mix well.
Pour pumpkin filling into hot or cool crust. Drop rounded tablespoons of the reserved cheese mixture onto the pumpkin filling. With a knife tip, swirl to marble the white and orange mixtures.
Bake in a 325° oven until the center barely jiggles when cake is gently shaken, about 50 minutes. Cool on a rack. Cover and chill until cold, at least 2 1/2 hours. Run a knife between cake and pan rim; remove rim.