Working from North to South is nearly always a good idea so you have a good start!
I'd suggest going to Florence after Venice since its a much shorter train ride.
This breaks up the long journey to Cinque Terre. Italy doesn't look that wide on a map but its a fair distance. Plus the railways don't have a direct route into the Cinque Terre the way you'd think they would.
You may want to opt to do Cinque Terre OR Sorrento but not both on this trip. Do you prefer remote laid back seaside towns (Cinque Terre) or the many day trip options available in Sorrento - to Pompeii, Naples, Amalfi Coast?
Here's 3 possible itineraries:
Option 1:
3 nights in Venice (Note: you'll lose 1/2 a day due to waiting on customs, getting to your hotel, checking in and getting settled)
Evening train to Florence on the 3rd day (2 hrs)
3 nights in Florence
Morning train to Cinque Terre (3-4 hrs) - This will take a better part of a day since you'll be checking out of one hotel, arriving early to wait on the train, checking into a new hotel etc.
3 nights in Cinque Terre (allowing 1 day for the above train travel)
Morning train to Rome (4+ hours so again allow a full day for checking out, train ride and getting settled in the new hotel)
5 nights in Rome
Option 2
3 nights in Venice
Evening train to Florence on the 3rd day (2 hrs)
3 nights in Florence
Morning train to Rome (4+ hours so again allow a full day for checking out, train ride and getting settled in the new hotel)
3 nights in Rome
4 nights in Sorrento (allowing 1/2 day to get to Sorrento)
Final day train back to Rome for flight home
Option 3
4 nights in Venice
Evening train to Florence
4 nights in Florence
AM train to Rome
5 nights in Rome
Note: For many travelers it would be easy to spend a week each in Venice, Florence and Rome and still not see everything they might wish to see. So examine the guidebooks on these cities very carefully before you decide to add Sorrento or Cinque Terre to the itinerary.
One of the easiest travel mistakes to make is to plan too many cities. :) You always have the option of taking day trips or "adding" another city while on the trip if you've accomplished all you'd hoped to see in one town or if you decide you don't like that town (unlikely!).