Strasbourg is the city where France and Germany have been arguing and borrowing from each other for a thousand years. It was a free imperial city of the Holy Roman Empire, became French in 1681, German again from 1871 to 1918, French, then German again during the Nazi occupation, and French once more since 1944. You can read every one of those chapters in the street plan. The old center on the Grande Île, a UNESCO World Heritage Site since 1988, is all half-timbered houses and canals. Across the river Ill, the Neustadt that the Germans built after 1871 is all wide boulevards and imperial domes.
It's a smaller, calmer and more interesting city than its size suggests. About 294,000 people live in the city itself, and they cycle, study and eat flammekueche in places that call themselves winstubs, wine taverns with German names and French menus. It also hosts the European Parliament, the Council of Europe and the European Court of Human Rights, which gives a medieval town an odd second life as a diplomatic one. Five days is the right length because Strasbourg itself needs about three, and Alsace needs the other two: Colmar and Eguisheim on one day, the castle of Haut-Kœnigsbourg and the Wine Route villages on another.
The plan goes day by day. Day one is the cathedral and the old center, day two Petite France and the water, day three the Neustadt and the European quarter, day four Colmar and Eguisheim, day five Haut-Kœnigsbourg, Riquewihr and Kaysersberg. Start on a Tuesday if you can. The astronomical clock runs at 12:30 on weekdays but not on Sundays, the Palais Rohan museums are closed on Tuesdays and the Œuvre Notre-Dame museum on Mondays, and this order puts every closing day on a day when you're somewhere else. More on the country is on the France page. The TGV from Paris takes under two hours, so Strasbourg pairs well with five days in Paris, and from across the Rhine Freiburg is about 85 km away.