5 Weeks in Belgium and the Netherlands

Brugge or Ghent or Atwerp can serve as base cities to take day trips from each to each.
I like Dinant in Belgium

Check out Haarlem near Amsterdam the church there is nice has an organ that supposedly Mozart played on.
Try Kinderdijk near Rotterdam to see and tour old wind mills.

With 5 weeks a couple of days or so in both in Gent and Brugge will be great. Antwerpen needs a little time too. Just north of Antwerpen is Bergen op Zoom, Netherlands which I like very much, and would work for the Antwerpen area. Allow enough time in that area too.

Driving in Belgium and the Netherlands is expensive (and trains are very cheap, especially in Belgium) because although there are no road tolls or vignettes, parking is rare, hard to find, and expensive.

The price of fuel is much lower in Belgium than in the Netherlands which contests with Italy for the most expensive in mainland Europe.

With so much time you can visit the more remote places much overlooked by most foreign tourists. To recommend is using the train/public transport for daytrips to cities and nearby places like the windmills of Kinderdijk. For more remote places you need a car.

In the Netherlands much overlooked is the eastern part of the country. If your base will be Amsterdam you can make a multiple day drive around the IJsselmeer, the big lake splitting the northern half of the Netherlands in two. Absolute lovely is Friesland with it’s distinctive character and why not visiting one of the Waddenzee islands. The historical cities along the river IJssel like Kampen, Zutphen and Deventer are worth a visit as well as the country side there.

The Delta region is interesting for seeing the Deltaworks and some quaint old cities too like Zierikzee, Middelburg and Veere. The massive Maeslant Barrier west of Rotterdam is not so easy to reach with public transport so you can combine it with a visit to the Delta Region for which a car is necessary.

Besides the larger cities in Belgium worth a visit are coastal resort De Haan and Ypres for the WW1 battle sites, for the latter you need a car or join a tour, some start in Bruges. Mechelen, Leuven and Lier are of interest and open air museum Bokrijk, between Hasselt and Genk east of Antwerp.

In Wallonia, the French speeking part of Belgium Doornik/Tournai and Bergen/Mons south-west of Brussels are both lovely places to look for. Dinant is popular and more east Bouillon with it’s medieval castle too. Bastogne for the Battle of the Bulge if that is of interest. Worth considering is adding a few days in Luxembourg (the country) with nice places like Esch-sur-Sûre and Vianden.

With those luxurious five weeks you can make a large loop, exploring cities and areas which are commonly overlooked.
At the start of you trip I prefer Gent above Brugge, being itself a lively city and only 30 mins from Brugge and Brussels, and with Antwerpen and amazingly attractive Mechelen (Malines) also within easy reach.
I am not very familiar with eastern Belgium (the Ardennes), but once found Mons (in the Dutch-speaking part of Belgium known as Bergen) a nice city. On the Dutch side of the border you'll love Maastricht.
After that you won't go wrong with exploring the string of the historical former Hansa cities along the IJssel river. Zwolle would make a good base, from where Zutphen, Deventer and Kampen are within easy reach. This area also a nice collection of country estates, such as in Ruurlo, Rijssen and Heino. Not really castles, but they come close.
Before going to your final destination, a few days in the north can't go wrong. Have Leeuwarden as a base for those smaller Frisian cities such as Sneek and Franeker.
Instead of crowded and expensive Amsterdam, you can have your accommodation in Haarlem. It's only 15 minutes from Amsterdam on very frequent trains, and has a direct bus connection with Schiphol airport.
As for transport, although both Belgium and the Netherlands have an extensive public transport network, reaching the most out of the way places and the train is the only reasonable option for reaching larger cities, a car would obviously come handy for exploring more rural areas.

PS.
While typing Wil had some similar ideas.

It's too much to reply for five weeks of travel, so I'll mention two stops we made on two separate trips. They were both drives from east to west, one from Venlo to Amsterdam, and one from Cologne to Antwerp. I would note that the food is better in Belgium, and the driving is easier in the Netherlands (except inside big cities.) I would use trains in the more popular parts of Belgium, since the car will cost you time. Roads are just as crowded as the suburban USA, and narrower. In both cases, you will be shocked at how small the parking spaces and ramps in the indoor garages are.

We slept in Arnhem because there was a modern business hotel right beside the Rhine river, an "NH" chain. (It came with earplugs, a shock, but luckily the few freight boats we saw were quiet. This allowed us to park in the (limited) hotel spaces near the hotel. Besides walking around Arnhem, we used the car to visit Deventer, Het Loo palace, Hoge Veeluue (sp?) park and art museum, and Nijmegen. We had already visited Amersfoort by train on a stay in Amsterdam. I'm interested in the idea of Kleve, but I was unable to determine that there is any remaining royal history to be seen there.

In eastern Belgium,we stayed at a (forgettable) luxury resort called La Butte aux Bois, driving to Tongeren, Bokrijk, Diest, and the open air musuem in Bokrijk. I can't remember if we went to Hasselt. We should have considered Maastricht. I really would not want a car between Brussels and Brugge. You'll be sorry is you use one there. I have often mentioned here the smaller towns of Lier, Mechelen, and Leuven. While it is less important, I like Turnhout because of the nice sense of a prosperous, happy (modern) town. When I was last there, it was still possible to walk around the Art Deco town hall without a security check, and the cathedral has wonderful woodwork. Be sure you check and reserve special Sunday-only attractions, like the town abandoned to build the new Antwerp port, or certain Town Halls that are only toured on Sunday afternoon (tickets at the TI.) Antwerp has lots of great museums, but the major KMSKA remains closed until 2019.

Edit: Here are some relevant older discussions:
https://community.ricksteves.com/travel-forum/belgium/day-trips-from-bruges
https://community.ricksteves.com/travel-forum/general-europe/getting-to-breendonk-memorial-belgium
https://community.ricksteves.com/travel-forum/belgium/trip-to-belgium-70d2c469-fbe0-4ff5-8237-d283b2dbd224
https://community.ricksteves.com/travel-forum/to-the-west/trip-to-belgium-a8c529ca-f305-4475-8e27-801e810b24e4

See "The Hiding Place" thread in the "Recommended Books" forum on this site (https://community.ricksteves.com/travel-forum/books-movies/the-hiding-place). It is about the Corrie Ten Boom House in Harlem.

With five weeks — and an interest in small towns, castles and quirky places — you might consider a slight expansion of your route to include Luxembourg and a bit of Germany.

We did this trip over 4 weeks in 2014 and it was fabulous — such a variety of places and scenery.

We too flew into Brussels, and stayed in Brugge with day trips to Flanders Field & the coast.

Then we visited Luxembourg, staying in Diekirch, but I’d recommend Ettelbruck instead as a base. Lovely little town. There is a pretty castle in Vianden & the famous Family of Man photo exhibit in a chateau in tiny Clervaux. Even though you aren’t museum lovers, Diekirch has a very untraditional and amazing WWIl museum filled with memorabilia, equipment, dioramas — all authentic items left behind in fields after the war. Ettelbruck has a Patton museum too.

We moved on to Germany, staying in Boppard on the Rhine, visiting Marksburg Castle and taking a scenic “Rhine cruise” on a ferry from Bingen back to Boppard ... where you’ll see the best collection of castles in Germany. We also spent a couple of days in Ernst, along the Mosel.

Then we made our way to Amsterdam, spending a full week there with some day trips. With a car and more time, you could see more of the Netherlands.

I know this goes beyond the scope of your original question but it was such a wonderful trip that I wanted to share our itinerary as an option.

You might have a look at Namur. It has a great castle. The guided tour (not required) includes the tunnels underneath the fortress. There are some nice churches in town as well. It's a train ride from Brussels.

A little further off your original request is the AtlantikWall at Ostend. Coastal fortifications from World War I and World War II, in remarkably good state. Think of it as a Twentieth Century castle. You can take the coastal tram from the railway station.