Chamonix is where people first went to look at the Alps for pleasure. English travelers visited the Mer de Glace in 1741, a doctor and a crystal hunter made the first ascent of Mont Blanc on 8 August 1786, local guides formed their own company in 1821, and the town held the first Winter Olympics in 1924. The cable cars still start in the middle of town, and the mountain behind it is the highest in Western Europe.
It is a better place to look at mountains than to ski them on one ticket. The valley has four ski areas that don't connect: Brévent-Flégère above the town, the Grands Montets at Argentière, Balme at Le Tour and Vallorcine, and Les Houches at the western end. The skiing is real, steep and big, but you plan around buses, lift closing times and weather. That is why five days works: three for skiing, one for the Aiguille du Midi, one for the Mer de Glace and the town.
The plan starts on a Monday. Days one to three are the ski days (Brévent-Flégère, the Grands Montets, Balme), so a three-day pass covers them. Day four is the Aiguille du Midi and a hard look at the Vallée Blanche, and day five the Montenvers train, the Mer de Glace and the new Mont-Blanc Museum, which is open on Fridays. The Aiguille du Midi is closed until 18 December, which rules out earlier Mondays, and the Mondays of 21 and 28 December are a trap: day five would fall on 25 December or 1 January, when the museum is shut. The first clean start is Monday 4 January 2027. The Vallée Blanche is listed with guides only from late January, so before then day four is the summit terraces alone. For a city before the mountains, see 5 Days in Lyon and the rest of France.