We typically like to spend a week or so in cities to see sites unrushed, with usually for a day trip away. Is there enough to see in Athens for 4 or 5 days, allowing for a day excursion to Santorini?

I"m so glad I gave Athens 4 full days, and I was on the move every possible minute of those days! i could easily have used more time there. Of course, YMMV.

BTW, I'm not sure a day excursion to Santorini is your best choice -- Santorini can be quite unpleasantly overrun by tourists during the day, Your trip, your call!

If you haven't already seen it, you might find some useful information in my trip report. The section on Athens is near the end.
With Gratitude for a Glorious Solo Month in Greece

We recently spent almost three full days in Athens at a slower pace (owing to DH recovering from an ankle injury) and felt that one more would have given us the opportunity to venture further afield. My trip report is here if you are interested in the specifics.

The Gods Were Ever in Our Favor

You won't be able to see it all, far from it. Athens is the kind of city you never tire of. From Athens we went to Delphi (fantastic) passing through the Corinthina canal (breathtaking). We rented a car - pay attention I've never seen so many car accidents on such a short trip.

Two way air fare to Santorini will make a very expensive day trip, and Santorini Airport is hopelessly inadequate for the summer invasion. You don't say what time of year you will be going, but Santorini won't be all that crowded from November until the following spring. Were it me I would consider Delphi or Nafplio and make it an overnight instead.

Four or five days will give you an opportunity to see what most of people go to Athens for plus other areas like the Central Markets, Anafiotika, Psiri District and lots more.

Check out this website for what to do in Athens:

https://www.athensguide.com/

A day trip to Santorini probably isn't worth the effort. You'll spend more time getting there and/or waiting for a flight than on the island.

A real nice day trip from Athens is the island of Aegina, very close to the mainland. From all accounts it's a lovely island with lots to do and will take only 40 minutes by Flying Dolphin or 1 1/2 hours by regular ferry. You can leave in the morning, spend several hours on the island and get back late afternoon . . . still in time for a night out in Athens.

On our second trip to Athens we spent a morning with Kostas of Athens Walks on a city food tour. Highly recommend it! Athens-Walks.com

I would echo what other's have said, going to Santorini for just one day from Athens doesn't make sense. While there is plenty to do in Athens for a week I also think you can see enough in three days to check all the major boxes and take the other day or two to spend more time in Santorini.

I just recently came back from Athens, here's my write-up of what I did for a weekend.

Why not spend a day or two in Hydros which is a charming island which is just an hour ferry ride away from the port of Athens.

Enjoy the unique sight to Santorini by entering the caldera on board of a slow ferry from Piraeus or forget it. It doesn't make sense to waste 6 hrs in planes, airports and metro trains in order to see almost nothing but foreign tourists.
Santorini must be seen from the Sea, not from the airport.