Preheat oven to 425°F. Make pastry: Pulse cake flour, baking powder and salt in a food processor until blended. Add cream cheese and butter and pulse 15 times, or until mixture resembles coarse crumbs. Transfer to a mixing bowl. In a small bowl, stir together 2 Tbsp. ice water and lemon juice. Add to dry ingredients and mix with a fork just until moistened and dough begins to hold together, adding up to 1 Tbsp. water only if necessary. Dough will be dry and crumbly but should hold together when a small amount is pinched between your fingers. Gather dough into a ball and flatten into a 4-inch disk.
Roll out pastry between 2 sheets of wax paper into a 12-inch round and transfer to a 10-inch fluted tart pan with a removable bottom, pressing gently into pan. Refrigerate.
Make filling: Combine brown sugar, flour, five-spice powder and salt in a large bowl. Add apples and toss to coat well. Spread apples evenly in tart shell.
Make streusel topping: Stir flour, sugar and butter with a fork in a small bowl until crumbly. Sprinkle over apples.
Bake until crust and topping are brown and apples are tender when pierced with a fork, 50 to 60 minutes. Let cool on a rack before serving.