Having just done a wonderful Med cruise in October with Princess, I have to concur with those who say a child of that age may be underimpressed. The port days, 5 in a row on my cruise, can be exhausting for adults because tours tend to be long, and the actual ports in some places are a LONG bus ride from the actual city you are scheduled to visit. For example, it was about a 1 1/2 hour ride from Civitaveccia to Rome, and about 45 minutes from Livorno to Florence. I can't imagine what it would be like for a 5 year old, who may quickly tire of and become bored seeing the best historic sights. When we had a sea day, it was almost like having a day off from work. LOL!
With the huge crowds, a little one will be seeing lots of other people's legs and maybe not much else!!