Ideas for a college student traveling from Copenhagen to visit Sweden for 4-5 days

With 4-5 days, she could easily spend the entire time in Stockholm. But it really depends on what interests her, and you don't provide any clues. Just hitting the typical tourist highlights within the city will fill a couple of days easily. Surely you don't need anyone here to advise you on what those are, as they are all covered in guidebooks or via a Google search of "top sights in Stockholm." If you expand the "At a Glance" section of the page at https://www.ricksteves.com/europe/sweden/stockholm, you'll get a list of Rick's top sights in Stockholm.

When I was in Sweden, I also visited Kalmar. It has a very cool-looking castle. Check out https://www.ricksteves.com/europe/sweden/kalmar.

And you should also expand the "At a Glance" section of https://www.ricksteves.com/europe/sweden for more suggestions.

STOCKHOLM:
We took a boat trip out to Fjäderholmarna – an island in archipelago about a 30 minute trip. Leaves often from Nybroplan in central Stockholm. Good restaurant on the dock out there.
Favorites were Vasa Museum, Drottingholm Palace, home to Royal Family. We went there by boat on Lake Malaren. Beautiful grounds.
Also City Hall, take a tour. Quite of bit to see there that you would not expect.
Millesgarden, a Sculpture Garden created by artist Carl Milles on the grounds of his waterfront home. It is out of the city center but easy to get there by subway and bus. We bought transit passes when we arrived which covered all forms including ferries, trams, buses, subways.
Stockholm is a beautiful city, our favorite in Scandinavia.

It really depends on what she wants to see/do. If she is studying in Copenhagen starting in Malmö seems like a bad idea, if she wants to see Malmö it is an easy day trip from Copenhagen. Although for a day trip to a Swedish town, Helsingborg, Lund, Ystad or Simrishamn are in my opinion more interesting. If you can be a bit more precise I can probably give better advice, but "old/historical stuff" is a bit vague. She can easily spend 4-5 days in Stockholm, or in Gothenburg, or hiking in the mountains. For older towns, Visby is also worth a few days. Uppsala should also be mentioned, lots of "old stuff" but as a student she can also get access to the student pubs and restaurants.

If she is interested in a trip a bit later in the year, she could head north and watch the Northern lights. They are beautiful, and as an astronomy student she might appreciate them even more.

Norwegian Air Sweden has flights for less than $100 (one-way) between Copenhagen and Stockholm.
Your daughter should sleep in the Gamla Stan (old town) and take Rick Steve’s self-guided walking tour. She should also visit Skansen (open air museum) and the Vasa Museum (warships) one day and take a cruise of Stockholm’s Archipelago another day.
I don’t know anything about Malmö, but one advantage of going there is you can take a direct train to Stockholm, there’s even an overnight train departing at 11:09p arriving the next morning at 6:14. If traveling during the day, it will take 4h 30m.
The train ride between Copenhagen and Malmö takes 45-minutes.

Norwegian Air Sweden has flights for less than $100 (one-way) between
Copenhagen and Stockholm.

Or she can take the train for less than 200 kr (≈€20).

She can get a lot of local info from her fellow students. There will be students from Denmark (obviously), and Sweden and Norway, and they will have a lot better feeling for what might be interesting for her than people on this forum, who - though well travelled and highly intelligent - tend to be slightly older than the average student.