Ajaccio is the one place in France where a city wears an emperor like a local football shirt. Napoleon was born here on 15 August 1769, and the street signs, the squares and the airport still say so. The Genoese founded the town in 1492 around a citadel on a rocky point, and it stayed a sleepy, mid-sized port until Napoleon made it the capital of a single Corsican department in 1811. Everything wide and straight in the center, the cours and the boulevards, is a legacy of that.
It's a small city of about 76,000 people (2023), sitting on a gulf with roughly 2,700 hours of sun a year. That mix is why five days works: three days of city and coast on foot or by short bus rides, and two days out into the island. The honest part is this: Ajaccio is the base, not the whole of Corsica. The famous landscapes, the red rock of Piana and the Scandola reserve, are an hour or more away on mountain roads, and Bonifacio is much farther. Only day four really needs a rental car, and a second car day for the Parata is a convenience, not a must.
The plan runs day by day. Day one is Napoleon's old town and the market, day two the Palais Fesch and the town beaches, day three the Sanguinaires Islands and the Parata at sunset, day four a drive up the west coast to Cargèse, the Calanques de Piana and Porto, and day five the mountain train to Corte. Start on a Saturday if you can: Monday is the weak day here (the market and the Maison Bonaparte are closed), so it becomes the outdoors day. Corsica is a very different place from the rest of France, and it takes a day or two to tune in.