Purée together the fruit, sugar, Chinese five spice powder and lemon juice in a blender. Taste and add more sugar and/or lemon juice if necessary; err on the sweeter side, as the sorbet will taste less sweet than the purée after being chilled. If necessary, add water 2 tablespoons at a time to help the fruit mix. If you’re using mango or seedy berries, strain the purée through a fine-meshed strainer, stirring and pressing on the mixture with a rubber spatula to leave any fibers or seeds behind; be sure to scrape all the purée from the underside of the strainer.
Cover and refrigerate until completely cool, then churn in an ice cream maker according to the manufacturer’s directions. Serve or transfer to an airtight container and freeze.