Five countries in 12 days... that's a lot! Hardly time for museums, unless you have special interests (apart from Amsterdam ).
Let's see, if you survive Amsterdam, you could then visit The Hague and Scheveningen, which is the coastal area of the city. I live there, so I'm not biassed at all! The Hague has the Peace Palace of course, the panorama mesdag, the government centre and you can go to Madurodam, which is a park with lots of authentic Dutch miniature buildings and countryside. Enables you to get a glimpse of the country in about an hour or so. (You can also drive through it in 2 hours, but then you'll probably only see grass, a few cows, highways and traffic jams.)
Belgium, Germany and Luxemburg... I don't know, but maybe someone here does...
France is easy. Go to Paris, look at or climb the Eiffel tower if you feel obliged to, but then visit the Place du Tertre. It's lovely, with little cafés and artists. Have dinner in Quartier Latin, a student area with lots of little cozy restaurants. The Louvre museum is too big I think, but taking a short tour might be possible.
The above is all pretty basic tourist material, so if anyone has to add to this, feel free