Combine five-spice powder, pepper, and salt in cup. Rinse chicken; pat dry with paper towels. Cut into 1-inch pieces. Rub spices onto chicken. Wash hands.
Heat oil in 2-quart stockpot. Add chicken and cook over medium-high heat until browned on all sides, about 5 minutes.
Add garlic to pot and cook until fragrant, 1 minute. Add chicken broth and soy sauce; cover and bring to boil. Uncover, reduce heat to a simmer, and cook 3 minutes. Add pasta; simmer 1 minute. Add spinach; stir just until wilted. (Refrigerate leftovers.)