Itinerary for Italy with a 5 year old kid

I traveled in Europe with pre-teens. My Son was 5 when we first visited the UK.

You won't be able to visit many museums with a child that young. They get bored in museums and let you know it.

My kids loved the gondola ride in Venice. Also, they loved the Sistine Chapel a lot. They wanted to know all about the figures in the frescoes.

Also, they loved the Coliseum in Rome for some reason.

Cinque Terre is nice, but a bit out of the way from what I consider the big three, Rome, Florence and Venice. I liked Sorrento, Capri and the Amalfi Coast better than CT.

We just got back from Spain & Paris with a mature 8 year old girl.
She tells everyone her favorite part of the trip was the Eiffel Tower and the art museums.
Funny thing is that her attention span in the art museums was about 15 minutes. She was ready to go.
We took time out to let her swim in the Mediterranean and go to the Barcelona Zoo. I suggest you look ahead of time for kids' things to do.

I have heard from friends who took their kids to the Amalfi Coast and they were bored.
She may enjoy Siena with it’s large Piazza or
Lucca which has a Park on top of the medieval walls.
Why not Venice? Crowds? Get off in a neighborhood there.

Tell her something about what you'll be seeing in advance, so she can be excited and looking for things she remembers from your conversations. Scavenger hunts of various kinds always work with my 5-year-old (how many windows are on the facade? How many paintings of horses can you find? etc). We found some museums with children's guides in English, but you could even make do with an Italian one. Stop for gelato every day and give her time to run around in open space. An agrotourismo in Tuscany would be good for that.