In the autumn of 1944, after the Warsaw Uprising failed, Hitler ordered the city wiped off the map, and German demolition teams went from street to street with explosives and flamethrowers. When the Red Army finally crossed the Vistula in January 1945, most of the left-bank city was rubble. Most of what you see today was built after that: an Old Town rebuilt brick by brick from paintings and old drawings, a skyline of Stalinist and glass towers, and memorials on almost every corner.
That makes Warsaw less pretty than Kraków and more interesting. It's Poland's capital since around 1600, a city of 1.8 million that works hard and goes out late, with some of the best museums in Europe, a riverside that comes alive in summer and a food scene that has moved far beyond pierogi. Weekend visitors see the Old Town and leave. Five days let you understand how the city was lost and rebuilt, which is the real story here.
This plan keeps each day in one part of the city, and it fits the museums' closing days best if day one is a Wednesday. Day one is the Old Town and the Royal Castle, day two the Royal Route, Chopin and Łazienki Park, day three the Jewish city and the Uprising, day four Praga and the river, and day five Wilanów Palace and the National Museum. If you have longer, Chopin's birthplace, the Kampinos forest and Łódź come after day five.