Davos has two reputations that don't sit easily together. In January the World Economic Forum brings some 3,000 leaders from business and government to town, and the rest of the winter it's a ski resort with a long and rather sad history: from the middle of the 19th century doctors sent people with lung disease here, led by Dr Alexander Spengler, and Robert Louis Stevenson wintered here in 1880. Thomas Mann visited his sick wife in 1912, and The Magic Mountain came out of it in 1924. The skiers came after the patients, and Arthur Conan Doyle was writing about skiing in Davos by 1899.
What you get today is five ski areas, a little over 250 km of pistes by the operator's count and one regional pass. Davos itself is a long, plain, practical town at 1,560 m, built along a valley, and it has the bigger share of the skiing. Klosters, half an hour by train down the Prättigau valley, is smaller, greener and quieter, and it is linked to Davos by the Parsenn mountain. Five days works because the five mountains really are different, and a day off the skis fits in without guilt: the Schatzalp funicular, the sledging run and the Kirchner Museum.
The plan starts on a Monday: Parsenn from Davos on day one, Jakobshorn on day two, Rinerhorn and Pischa on day three (a Wednesday, which is the night-skiing evening at Rinerhorn), Gotschna and Madrisa from Klosters on day four, and a day off the skis in Davos on day five, a Friday, when the Kirchner Museum is open (except 4 January to 13 February 2027, when it's closed for remodelling). If you'd like the other big name in the same canton, see 5 days in St. Moritz, and for everything else about the country, see Switzerland.