Are those cities enough for Poland?
Leave out £ódż, and spend more time in the other four, if you have 15 days, or in three of the other four, if you only have ten days. Yes, those would be the best "youth" cities, but only after the semester starts up at the beginning of October. Until then, a lot of the students leave these cities and go to their hometowns. However, all of those cities also have a lot of young tourists during the summer and fall, from Poland and from other countries.
If you absolutely are hell bent on seeing £ódż, you can easily do it as a day trip from Warsaw. It's only two hours away by train. Other easy day trips from Warsaw include Kazimierz Dolny, and from Kraków, Auschwitz and Zakopane.