Cinque Terre or Amalfi

Our time in the Cinque Terre in 2015 is one of our best memories of European travel. Many folks would say that 5 nights there is a lot, however we were there for 4 nights and would have happily stayed a fifth. The scenery is spectacular. We are pretty content with lazy mornings, long afternoon walks followed by early evening wine and a nice meal. If you would be happier with more to see and do, then maybe 5 nights is a lot. We also used the train from Florence and if I remember correctly, changed trains to accomplish this. Then there was the dragging of the luggage up 100+ steps...so it was nice to have downtime after an active travel day, and Florence, which was very crowded in June.

Do you have three nights each in Rome, Orvieto, Siena farm, and Florence? I think all of those could warrant more time if adjustments can still be made.
If you are avid hikers, then five nights in CT will not feel like too much. If it rains, it will feel like too much, but there are towns along the train line to visit if you get bored.
If you are not into hiking or are just concerned about crowds, then there are plenty of other coastal places where a week would be divine.

If you only have 3 nights in Rome with 1 day being arrival jet lag day I’d add at least 1 to Rome, 2 would be better

Haven’t been to CT but have been to Sorrento/Amalfi area and are returning again this Sept
There is a lot to do in that area
Naples, Pompeii, Sorrento itself, Capri, Amalfi coast towns, Salerno/Paestum
We spent 9 nights in the area and still want to go back so will spend another 4 this time

I'd agree that three nights in Rome is extremely short when you have (apparently) about 20 nights to work with. My first priority would be to adjust that. Since you have to be back in Rome at the end of your trip for the flight home, you could add on to the final, single night there without affecting the rest of the trip.

My trips to Cinque Terre were too long ago to provide me any sense of what the area is like now, but I've read the same "it's grotesquely overrun" comments you've probably seen here. However, the views from the ferries should still be spectacular, and even if some of the Sentiero Azzurro trails are still closed next year (highly likely, I'd guess), you should be able to climb up high enough to see some great views. As already mentioned, there are other, less swamped, places along that stretch of coastline should the situation in the C.T. be too much to bear: Camogli, Bonassola, Santa Margherita Ligure, Portovenere, Lerici, Tellaro... Some of those would require train+bus from the Cinque Terre.

Should you run into unpleasant weather that makes indoor sightseeing a very attractive option, you could head to Genoa. I'm currently researching northern Italy for a future trip, and I've found a very long list of things to see in Genoa. Genoa's about 1-1/2 hours from Monterosso by train--not ideal, but doable.

There's quite a lot to see in the Amalfi area, but I'm not sure how much time you'll have left if you increase your total number of nights in Rome. Pompeii takes the better part of a day, as does Capri.

Amalfi Coast (also Capri, Sorrento and Pompeii) has it all over CT.

Rome deserves several night, so much to see. Also, Florence a minimum of 3.