Put a small plate in the freezer.
In a 4- to 6-qt. pot over medium-high heat, bring tangerine zest and juice, sugar, ginger, pepper, and five-spice powder to a boil. Add cranberries and cook, stirring frequently, until they pop and bubble up and the juices thicken, 5 to 10 minutes.
To test sauce, spoon a little onto the frozen plate. If the surface wrinkles and you can draw your finger cleanly through the sauce, it’s done. Remove from heat and let rest at least 3 hours before serving so flavors can harmonize.
*Available in the spice aisle of most grocery stores.
MAKE AHEAD: Up to 3 months, chilled.