Sapporo is not an old Japanese city, and it doesn't pretend to be. Hokkaido's capital was only picked as a site in 1868, the Hokkaido Development Commission set up here in 1869, and in 1870-71 the commission brought in an American adviser, Horace Capron, to help lay it out. The result is a grid of straight streets and numbered blocks, a wide park down the middle and almost no temples. It's also the city that hosted the first Winter Olympics in Asia, in 1972, and today it has close to two million people.
What it has instead is winter. Sapporo is one of the snowiest big cities in the world, the sun sets around 4pm in midwinter, and the whole city leans into it: lights down Odori Park from late November, a Snow Festival in early February, and a food scene built for cold weather. Miso ramen was invented here, so was a spicy soup curry with a chicken leg in it, and lamb grilled on a dome-shaped pan is the local party meal. Five days is the right length because the sights are spread out and the food is the real itinerary; two days covers the postcard, five lets you eat your way through it and still get to Otaru.
The plan keeps each day to one side of town. Day one is the center, day two the west, day three the east and the beer, day four a day trip to Otaru, and day five the northern edge and the big park. Start on a Tuesday: that puts Otaru on a Friday, when the cheesecake cafe takes seat reservations and the town is quieter than at the weekend, and it keeps Monday free of the museums and the Glass Pyramid that close then. If you want serious skiing, Niseko is about two hours away. The country basics are on the Japan page, and the capital has its own 5 days in Tokyo plan.