Hi nathalie, i live in rome so i could suggest you that 5 days in Rome are few to visit all the monuments, vaticano, historical center (piazza navona, piazza del popolo, pincio, fori,trastevere...). However if this trip is your first in italy, napoli, and maybe costiera amalfitana, is mandatory!
On the other hand there is an other opportunity,
you could visit Rome and the little towns near Rome, known as roman castle: Frascati, Ariccia, Albano. They are connected to rome by train and by bus. They are chiper then rome and you could find the original rome cucine!
So if you prefer sun and sea better neaple, if you prefer monuments and food better rome and roman castle!
Godd Luck!