Hamburg

A number of ideas and MarkK's post has a list.

https://community.ricksteves.com/travel-forum/germany/things-to-do-in-or-around-hamburg-germany-as-well-as-berlin-and-dresden

There are a number of other posts as well from the past several months - search "Hamburg" in the Germany section
https://community.ricksteves.com/travel-forum/germany/stopping-in-hamburg-on-a-cruise-would-should-i-not-miss

Hard to recommend without knowing your interests. Lots of on-line guides for starters. Many will be glad to help with more specific questions.

Great that you have 5 days set aside for Hamburg. I went there on the first trip in Germany too, unthinkable not to see Hamburg. I had then 3 full days. It was my second German city to be visited after exploring and seeing the first , Lübeck.

If your interest lies in the historical field , number of sites are very interesting. just depends on your level of interest in that field.

Hamburg's annual May highlight is the harbor birthday - this year starting on Thu, May 9. The parade of incoming ships is zje special top of the event. Weather is forecasted as nearly perfect, little more wind would be nice.

Besides the lists and ideas in the already posted links (thanks to ORDtraveler) and Fred's Lübeck tip also other day trips can be attractive, e. g. Schwerin (castle, beautiful lake and old town), Wismar (old town), Bremen, and Lüneburg.
Special day rip is boat trip to Helgoland island but can be shaky at strong

For foodies the Altes Land area around Jork (south-west of Hamburg) is a must-have to taste apples. Close to it is Stade, a small beautiful old town. Airplane lovers visit Airbus also there. All in reach by public transport (HVV).

Any special interests?

Miniatur Wunderland......the reason I visited Hamburg.

Seconding Miniatur Wunderland - even if you think it’s not for you. It’s amazing.

Lübeck is an easy and beautiful day trip by train. Such a gorgeous historic centre.

Oh, so much!

DEFINITELY try to catch a musical if you can. Small and local, big and famous, we have it all. A concert in the Elphi would also be a great choice.

Ride the ferries. Hamburg should be seen from the water, and a ferry to Finkenwerder takes you past the Blankenese area on the water side. Speaking of Blankenese, walk through the Treppenviertel (stairs quarter) to the beach. Beautiful homes on a hillside, reed roofed and traditional, and then a walk along the beach (at low tide you can see the shipwrecks) and through the Watt. The best low tide is at the lighthouse in Wittenbergen, a bit of a walk along the beach. Great place to catch a sunset.

Boberger Sand Dunes are also a great and unusual physical feature. Highly recommend for some lovely nature walking.

The Tower Bar is a bit pricey, but offers great views of the city while you enjoy a cocktail.

I could go on and on and on--I have written so much on here, both on and off the beaten track. Search through some of my posts.

Here is one where I wrote a bunch of ideas:
https://community.ricksteves.com/travel-forum/germany/hamburg-worth-4-days-with-day-trip-to-lubeck-or-bremen