wpayos, as you didn't express any previous interest in the Cinque Terre or Pisa, I don't think you need to include them. Capri will require some transport time, and I'm not sure I'd do it unless you have some interest in, and time for, other parts of the region, such as Pompeii, Sorrento or Naples.
You haven't told us how you prefer to travel? Do you like to have more versus less time to browse around your cities of choice, or hit the highlights (those being of your choice) and move along? And what sorts of thing do you wish to see?
Without having answers to the questions above, if you can fly into Venice and out of Rome, I might do this:
Day/night #1 - overnight flight to Venice
Night #2, 3 and 4: Venice
Nights #5, 6, 7: Florence
Nights #8, 9, 10; Capri
Nights #11, 12, 13, 14: Rome
Day 15: Fly home
If you are a "slow" traveler and can leave out Capri (which is what I'd recommend), I might do this:
Day/night #1 - overnight flight to Venice
Night #2, 3 and 4: Venice
Nights #5, 6, 7, 8, 9 Florence with a day trip (Siena and/or Lucca)
Nights #10, 11, 12, 13, 14: Rome
Day 15: Fly home