To echo everyone else, 5 days is not enough to do multiple (even just two) locations any justice. To actually move city to city, you will waste a minimum of half a day - what with packing, checking out, getting to the train station, arriving you new city, FINDING your new lodging, checking in, and settling in. If the move is to a far-flung place, you could lose the better part of a day. Then, since your return flight is out of Rome (as indicated), you must repeat so there goes another half-day or more. I would just stay in Rome.
In order to help you out more, please provide some more details on you exact travel itinerary - where you are leaving from (DTW?), day you are leaving, when you are arriving Rome, and the day you are leaving Rome to return home. This information will help forum respondents to focus on the exact amount of time you have.
Why is this important? First, the vast majority of flights from the USA to Rome leave late in the day and arrive mid-morning to early afternoon the NEXT day. From Michigan, Rome is 6 time zones (hours) ahead. Second, certain venues are closed on certain days of the week.
Finally, Rome is a city of over 4 million residents and has over three centuries of history on display. It has so many "faces", you can't possibly do more than scratch the surface of this incredible city in a short 5 days. To make matters even more challenging, the top tourist venues may require standing in line for hours just to get tickets - unless, of course, you research what you want to see ahead of time and purchase your time-sensitive entry tickets on-line and well in advance.
Do yourself a big favor and go to the library/bookstore and read Rick's book on Rome. Or, purchase the eBook so you can carry it around with you on your tablet or smart phone.