Whisk together pumpkin puree, egg yolks, and egg in a large bowl until smooth. Add sweetened condensed milk, cinnamon, ginger, salt, nutmeg, and Chinese 5-spice powder; whisk until thoroughly combined.
Fit pie crust in a 9-inch pie plate and crimp edges.
Pour filling into the pie shell and lightly tap on the work surface to release any air bubbles.
Bake in the preheated oven for 15 minutes.
Reduce heat to 350 degrees F (175 degrees C) and bake until just set in the middle, 30 to 40 more minutes. A paring knife inserted into the filling, 1 inch from the crust, should come out clean. Allow to cool completely before serving.
