5 nights? or 6 nights?
I'm wondering the same thing as Christine. It's unclear exactly how many NIGHTS you'll have on the ground in Italy, and it makes a difference where what you'll be able to do is concerned. For instance, did you plan to visit Pompeii on your first FULL day in Sorrento? if so your itinerary would look like. this:
Night 1: Arrive Rome and train to Sorrento - sleep Sorrento
Night 2: See Pompei - sleep Sorrento
Night 3: See Naples - sleep Sorrento
Night 4: Move to Positano to stay and explore Ravello - sleep Positano
Night 5: See Capri and Amalfi town, sleep Positano
Night 6 train to Rome - sleep Rome
depart for home.
Hopefully you are not planning to do Pompeii en route to Sorrento, all jet-lagged right off an international flight: not a good plan. As mentioned above, Capri is more easily/quickly gotten to from Sorrento and takes an entire day to explore. Ravello is not on the coast and is done by bus from Amalfi. I'd skip Positano altogether and stay in Amalfi to do both that town and Ravello, or skip Naples and do Positano as a day trip from Sorrento. To return to Rome, take a SITA bus from Amalfi to Salerno and take the train from there.
If you only have 5 nights, something will have to go.