São Miguel is the biggest of the nine volcanic islands of the Azores, about 1,400 km out in the Atlantic, and people have lived here since 1444. The Portuguese call it a Ilha Verde, the Green Island, and it earns the name: pastures on every slope and crater lakes where a normal island would keep its mountains. It's also still a volcanic island. The ground steams in Furnas, locals cook dinner in it, and an earthquake in 1522 wrecked the old capital, Vila Franca do Campo, and handed the job to Ponta Delgada.
The island is only about 65 km long, so five days isn't about distance. It's about weather. Conditions change by the hour, the famous viewpoints vanish into cloud for half the day, and a place that was white at ten can be postcard-clear at three. This plan gives each day one part of the island, a rain plan, and a rule: if the lake you came for is in fog, swap the day and go to the hot springs instead. A car makes that possible. Without one the island shrinks to a few towns and the bus timetable.
Day one is Ponta Delgada, a lava tube and a pineapple plantation, with a whale-watching trip early on so a canceled boat can be rebooked. Day two is Sete Cidades and the west, day three Furnas, day four Lagoa do Fogo and the north coast, day five the wild northeast. Start on a Tuesday if you can: the city market is closed on Sunday, the fort museum is listed as open Monday to Friday by one source and Tuesday to Saturday by another, and the Vila Franca pastry shop on day three keeps weekday hours. The other islands are in the last section, and the country page has more on Portugal.