Updated Itinerary, Good Now?

Nice, relaxed pace to the itinerary. I like it. You may find you can quickly cover Day 4’s Pantheon, Spanish Steps ( don’t sit on them or you could be fined)! and the Trevi Fountain all before lunch since it’s only a one mile walk between all three sites. That would free up the rest of the day. And that could allow you to wrap up Rome earlier than expected or explore more of the Eternal City. It also could open up time on the A.C. So you can make it to Amalfi Town and its neighbor, Atrani.
Have a great trip!

One question or suggestion..what are you doing with your luggage if going directly to Pompeii from Rome before going to hotel in Naples.

In Rome I suggest getting tickets for the Borgessi Gallery ..amazing art which you must have a timed entry ticket for. Also we did the golf cart tour at night in Rome and the Hop on Hop off bus in Naples ..would recommend both.

There is luggage storage at both the Pompeii Scavi-Villa dei Misteri train station under the tracks, and at the Porta Marina gate entrance.to Pompeii.

Looks good. I was just in Rome and Naples and have a few ideas.

If you could split up the Colosseum and Forum into two separate days, you get to enjoy both more. So, for example if you get the 24 hour ticket, and go to the Colosseum at 10am day 1 and the forum 9am day 2, you can see the forum totally empty without any crowds. I also recommend the foro romano entrance on the South side. It’s closest to the parts of the park that get crowded too.

Also, National Roman Museum is empty if you go around 5pm and it’s amazing. I don’t know why people leave it off their itineraries in Rome.

I’m also a fan of spending more time in Naples. It’s an amazing city. It has a bit of an element of challenge with the traffic and hectic nature of the city center, but I loved it. If you get to Chiaia and Vomero and the waterfront it’s really lovely. And the food is amazing.

You should go to Herculaneum as well if you can. If that means not going to Capri and spending some extra time in Naples, I think it’s a good trade off.

Looks good as far as not trying to do too much but you might think about grouping your sightseeing in Rome more geographically? A few for-instances/additions for these three days:

Day 2 Rome - Booked tickets to Vatican Museums and St. Peter's Basilica, Jewish Ghetto, maybe Aqueducts later.
Day 3 Rome - Colosseum, Forum, Basilica Santa Maria
Day 4 Rome - Pantheon, Trevi fountain, Spanish Steps

OK, Day 2: The Ghetto and aqueducts are in completely different parts of the city than the Vatican, which is on the northern side. The Spanish Steps are also on on the northern end so you might want to walk directly east of Vatican City after your visit, passing Castel Sant' Angelo and the Sant' Angelo bridge with its wonderful angels, and onward to the Steps.

Consider as well the Trevi and the Steps have no hours/admission fees so don't HAVE to be done between any specific hours.

Day 3: I sincerely hope you're also including Palatine Hill with the Colosseum and Forum. If you haven't already, I'd strongly consider a guided tour that include all 3 sites (they usually run between 3-4 hours) as Forum & Palatine are much more complex sites to understand without one. If you look at a map, you'll see that the Jewish Ghetto is located almost directly west of that group so that's what I'd combine with them. You might add a look at Michelangelo's Piazza Del Campidoglio along the way.
https://www.turismoroma.it/en/places/piazza-del-campidoglio-capitoline-hill

Day 4: Now you have the middle of the historic center. Attractions, from east to west, that you could group would be Santa Maria Maggiore, Trevi Fountain, Pantheon, Piazza Navona, Campo di Fiori and Area Sacra di Largo Argentina, give or take.

Day 5 is the day you could head further south of center to the aqueducts (Parco degli Acquedotti). I'd try to include parts of the Appia Antica, if possible, as it's in the general vicinity. Maybe an e-bike tour that combines them? Rick Steves gives this company a thumb up, and they offer a group or private tour of either 4 or 6 hours in length. The 4-hour version skips a visit to one of the ancient catacombs, which we personally found very interesting but might not trip your trigger.

https://www.topbikerental.com
https://www.topbikerental.com/rome-bike-tours/appian-way-catacombs

If I've counted correctly, your Day 5 falls on Sunday, October 5th? That's perfect for the Appia as it's largely closed to vehicular traffic on the Sabbath. :O)

Might use your arrival day to do a small wak-about. You didn't indicate where you were staying but I like the idea of walking to the Trevi fountain and Spanish Steps. No tickets needed so you do it at your pace if your jet lagged. I definitely wouldn't purchase tickets for arrival day. Just a suggestion..