Amalfi City or Sorrento

Where else are you going to be on your trip and what do you want to see/do in the Sorrento/AC area?

The ideal is of course to stay in the same place the whole 5 nights. If that is not possible due to Positano being booked everywhere, then your decision should be based on what you want to do during those extra days.
If you plan to visit Pompeii, Naples, Ercolano, the islands (Capri, Ischia, Procida), then Sorrento is logistically a better choice.
If you plan to visit more of the Amalfi coast proper, then Amalfi is a better choice.
But since you already have two nights in Positano, I would try to see if they can accommodate you for the additional nights in the same hotels.

If Amalfi is booked, you could try Atrani. It is a short 10 minute walk from Amalfi and might offer accommodations that might not be available in Amalfi itself. There is also Praiano, which is a just east of Positano. There is a small local bus that runs between the two as an option other than the Sita bus. Just some alternatives to consider....

If you plan on doing any sightseeing in Naples, Pompeii, Herculaneum or Capri then definitely book those nights in Sorrento. It’s ideally situated for these sights transportation-wise. If you’re just interested in relaxing on the Amalfi Coast then I would recommend a smaller town like Atrani/Priano/Maiori/Ravello. I thought Amalfi was kind of a moribund place more charming from a distance. Just to note, if Positano is all booked up it will likely be difficult elsewhere as well. Your next town of choice might be more dictated by availability. Don’t worry too much, it’s all pretty stunning and hard to go too wrong.

Sorrento is a better base for day trips, bigger, more to see and do.

Thanks everyone! We decided to stay in Sorrento so we could catch the train from Naples to Rome. I think this is a bit easier.