Position racks in the upper and lower thirds of the oven; preheat to 400˚. Whisk the flour, cream of tartar, 1/2 teaspoon each five-spice powder and cinnamon, the baking soda and salt in a medium bowl.
Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 4 to 5 minutes. Beat in the eggs one at a time until combined. Beat in the vanilla, then reduce the speed to low and beat in the flour mixture until combined.
Mix the red sanding sugar and the remaining 1/2 teaspoon each five-spice powder and cinnamon in a small bowl. Roll the dough into balls (about 2 tablespoons each), then roll them in the red sugar. Arrange 3 inches apart on 2 unlined baking sheets.
Bake, switching the pans halfway through, until the cookies spread, crackle in the centers and are lightly golden around the edges, 9 to 12 minutes. Let cool 10 minutes on the pans, then remove the cookies to racks to cool completely.