Berlin never finished being built, and that's the whole point of it. It has been the capital of Prussia, of the German Empire, of the Weimar Republic and of the Nazi state, then two cities behind a wall for 28 years, and since 1990 a capital again. Almost every street shows one of those chapters: a Prussian boulevard, a Cold War border strip turned into a park, a 1960s TV tower, a glass dome on a 19th-century parliament. Around 3.7 million people live in the middle of it, and a former mayor once summed the place up as arm, aber sexy, "poor but sexy".
It's also huge and spread out, which is why five days make sense. Mitte alone, with the Brandenburg Gate, Museum Island and the Wall memorials, will take two full days. Add Kreuzberg's food and Cold War sites, a day in Potsdam among Frederick the Great's palaces, and a few late nights. History here is told as it happened, including the parts the city is not proud of. Some of the best things in Berlin are heavy, and the plan balances them with beer gardens and long walks.
The plan: day one is the west and the government quarter, day two is Unter den Linden, Museum Island and the old center, day three follows the Wall through Prenzlauer Berg and Friedrichshain, day four is a trip to Potsdam, and day five is Kreuzberg, the Cold War checkpoint and the old Tempelhof airfield. Start on a Tuesday or Wednesday if you can: the plan is built around the Monday closures of most museums and of Sanssouci in Potsdam, and any other start day puts one of them on a Monday. Berlin is also a good way into Germany as a whole.