How many days do I need in Italy?

Ten to fourteen days for a first trip, and two or three bases rather than five. A week is enough for two cities done properly, or three done in a hurry. The mistake almost everyone makes is counting days instead of counting mornings: a travel day between cities costs you a morning packing, a middle in transit and an afternoon finding your feet, so a "day" in a fourth city is often four usable hours. If you only have a week, cut a destination rather than shortening every stay. You will not see Italy in one trip. Nobody does, including Italians.