I have a bias against Leiden. I used to love it, but then I stayed when the University was in session, town overrun with college students. I have no issue college students, but I thought the majority of the bars and restaurants skewed young in a way that catered to them. Though people were nice enough, I felt tolerated more than welcome.
The above is a matter of degree of course, but there are Dutch places I enjoy more.
I don't think I would do Rotterdam for 5 nights. I like Rotterdam - it's an interesting, diverse town. And it holds the auspicious distinction of being the only place I've ever seen people lighting parked cars on fire - exciting! If I'm in the Netherlands though and I'm spending a lot of time somewhere I want it to be more of the classic picture postcard than Rotterdam.
I also like The Hague and have visited several times. One thing about the Hague though is it a bit of a cul-de-sac. The sea is nice, but I've lived near spectacular beaches my whole life so spending a lot of time on a North Sea Beach doesn't really fire my jets. And the city itself is pretty dispersed. Good sites but feels more big city than I like.
Delft might be a good choice. It's just so incredibly pretty and quaint, and has a wonderful square. But it's small. Would make a comfortable base I think.
Gouda also might be a good call in the area where you're looking to stay. Gouda is equidistant from a lot of destinations. It's not as much of a fantasy movie set as Delft, but it is quite a pretty scene. It's bigger than Delft, but still a very manageable place to walk. I also like that Gouda is mostly surrounded by pretty countryside.
My pick though would be Den Bosch. It's a wonderful charming small city with a lot for tourists to do. It has a more vibrant sidewalk
cafe "good life" culture then most Dutch cities. It has a lot of boutiquey amenities, pretty shops, interesting restaurants, cool hotels. Gorgeous countryside all around it and lots of fun easy day trips. Since you're already going to Amsterdam for 5 nights you're going to get a lot of Holland - might be nice to see a different province.