The Faroe Islands are the kind of place where you plan the day around the sky, not the other way round. Eighteen steep, treeless islands sit in the North Atlantic between Iceland, Norway and Scotland, with roughly 55,000 people, more sheep than that, and a coast of cliffs, waterfalls and villages with turf roofs. They are a self-governing part of the Kingdom of Denmark with their own parliament, the Løgting, their own flag (the Merkið) and their own language, Faroese. The money is Danish kroner: the Faroese króna is not a separate currency but a local issue of banknotes at par with the Danish krone, so DKK works everywhere. Our longer introduction to the islands has the history; this guide is about what to do with five days.
The Faroes reward people who like to walk and drive, and they are not cheap, soft or predictable. Fog can close a viewpoint and wind can cancel a ferry. A car is close to essential, because the buses reach most villages but not on a schedule that suits a day of sightseeing. Many of the best-known walks now cost money, because they cross private land, and the amounts and the booking rules changed recently. That is why five days is the right length: four days of landscape and one flexible day, so a single bad forecast doesn't wreck the trip.
The plan is organized by geography. Day one is Tórshavn, the capital, day two Vágar and Gásadalur, day three the north of Streymoy and Eysturoy, day four Klaksvík and Kalsoy, and day five Mykines from May to August or Kirkjubøur and the National Museum for the rest of the year. Start on a Monday: shops close on Sundays, so you spend the quiet day on the road rather than in town. Between October and April the plan changes in places (short days, reduced ferries, museum hours), and each day says how. If you want the Danish side of the story, our page on Denmark covers the kingdom; just don't call a Faroese person Danish.