Advice on possibility of itinerary in short time available

You have five nights: Sun, Mon, Tue, Wed, Thu. Friday night is back in Rome.

I'd do two nights in Venice and three nights in Florence. Do a day trip to the Cinque Terre from Florence. One reason to do it that way is that depending on the weather, one day might be better than another in the CT. So you could choose Wed or Thur depending on the forecast that day. Could be both days are bad and you don't even bother.

It would of course be very tight with a lot of traveling, much of your time on trains. Up to you whether it's worth doing.

Instead of Cinque Terre, you could take in Lucca--a very popular place.

You're not trying to cram 3 places in in 2 days, so it's certainly doable, and will depend on how long you decide to visit each place. Are you planning on taking the train for all or part of the travel between those places? Or driving, or maybe a relatively-short-hop plane ride that still involves checking in, going thru security, etc.? Transportation departure and arrival times might affect your schedule or route direction choices (counter-clockwise vs. clockwise, so it could be helpful to look at what those might involve.

Florence and Venice are easy by train. The Cinque Terre adds a lot of travel time, but there's an 8:28 AM departure from Florence on weekdays that gets you to Monterosso (after two changes) at 11:17 AM. That's the option I'd choose for a day-trip.

ViaMichelin estimates the driving time (no stopping, getting lost, looking for parking, etc.) from Florence to Monterosso at 2 hr. 19 min., so that certainly wouldn't save any time after you figure you have to deal twice with a car-rental agency, plus there would be the parking issue to deal with.

I chose Monterosso at random from among the five towns to do the schedule-checking.

I would agree about going to Lucca instead. It is a magical little town.

With the time you have, I suggest 'pick 2'

Go to the farthest destination 1st and work back to Rome.

This is super helpful each one of you! Thanks so much.

I would definitely pick 2. Three involves too much traveling and not enough enjoying.
I would not do a day trip to Cinque Terre from Florence, though. You will arrive right when the throngs of tourists arrive. Cinque Terre is better early mornings and later in afternoon/evenings when the other day-trippers are gone.

I would not do a day trip to Cinque Terre from Florence, though. You will arrive right when the throngs of tourists arrive.

This will be in November. I'm sure the Cinque Terre still has tourists then but it shouldn't be so bad as in the summer and late spring/early fall.

Do 2, train Rome-Venice 3 1/2 hrs. Spend 2 nites. Then Train Venice-Florence
2 hrs. 3 nites. There are several towns under an hour ride. Bologna, Pistoia, by train, Siena by bus. Florence-Rome 1 1/2 hrs.

If this is too much travel, spend the 5 nites in Florence and do day trips from there.