I'm not sure if you're traveling by train or car, but let's assume you're going by train since all of these destinations are easily reachable. Leaving Rome, you could take the train to Florence, and base yourself there for three nights, spending the afternoon you arrive and the next day exploring the city and the next taking a day trip to Siena. You could certainly also add an extra day in Florence, depending on your interests.
The Cinque Terre (five villages) are about 2 ½ hours from Florence by train via Pisa. I've spent several days in the Cinque Terre, but I also visited the villages on a day trip from Florence a few years ago with relatives.
We were able to squeeze in a brief stop in Pisa, and arrive in the Cinque Terre in time for lunch and a walk before catching the train back in the early evening. It was a long day, and if you're really interested in exploring all of the villages, I'd recommend more time.
