Banff exists because of a hot spring. In 1883, railway workers building the Canadian Pacific line found the thermal pools at what is now Cave and Basin, and two years later the government set aside a small reserve around them. That became Canada's first national park. The Stoney Nakoda, who had used the springs and the valley for centuries, were removed from the park between 1890 and 1920. The railway built the hotels, the hotels brought the tourists, and skiing followed: Norquay opened in 1926, and it has been a ski town in a national park ever since.
Today the town is busy, expensive and very good at what it does. You get three ski areas that are unlike each other, all on one ticket and linked by free shuttles, plus a real mountain town to come back to. That is why five days works: four ski days cover Lake Louise twice, which it deserves, plus Sunshine and Norquay, and the fifth day is for what you can only do in winter here, like walking up a frozen canyon and skating on a glacial lake. It is cold and the days are short. It is also not cheap.
The plan runs Monday to Friday: Norquay on Monday, Lake Louise on Tuesday, Sunshine on Wednesday, Lake Louise again on Thursday, then a day off the skis on Friday. Fly in on Sunday and start on a Monday. Lake Louise and Sunshine fill up with day-skiers from Calgary on Saturday and Sunday, the Friday evening gondola at Sunshine and the night skiing at Norquay give your last evening something to do, and the Roam bus to Johnston Canyon ran only on weekends last winter, so Friday is a car or tour day anyway. More on the country is on the Canada page.