Wrocław has had more names and masters than almost any city in Europe. It was founded by Czech and Polish dukes, ruled by Bohemian kings and the Habsburgs, German-speaking for most of its history, taken by Prussia in 1741 and grew into Breslau, one of the great cities of the German Empire. In 1944 Hitler declared it a fortress. In January 1945 its civilians were driven out on foot into the frost, and many thousands died, and the siege that followed, almost three months long, left most of the city in ruins. Then the borders moved west, the German population was expelled, and Poles, many of them expelled themselves from what had been eastern Poland, arrived to build a new life in a city that wasn't theirs.
That's what makes Wrocław fascinating: a Polish city built on German foundations by people from somewhere else, who made it their own. It's also one of the most enjoyable cities in Poland: young, full of students, built on a dozen islands in the Oder with more than a hundred bridges, and with one of the most beautiful market squares in Europe. Most people come for a weekend. Five days let you see the islands, the museums and the countryside of Lower Silesia too. In 2016 it was the European Capital of Culture, and it shows.
This plan keeps each day in one part of town. Day one is the Market Square and the Old Town, day two the university and the islands up to Cathedral Island, day three the story of postwar Wrocław and Centennial Hall, day four the Racławice Panorama and the city's four faiths, and day five a trip to the Church of Peace in Świdnica and Książ Castle. If you have longer, the mountains and the other castles of Lower Silesia come after day five. Museums close on different days here (Mondays for most, Mondays and Tuesdays for the city museums, Wednesdays for the university), and the plan fits them best if day one is a Thursday.