Rent a car or hire a driver Florence to Rome and in between

Are you staying five days in one place, or are you talking about moving along over the course of five nights?
A lot depends on where you are staying and where you are going--could you add some more details?
You would need a very large vehicle or two vehicles, and it is not a good idea to leave luggage unattended in a car.

Staying near Siena and taking trips from there. Will not be leaving luggage in a vehicle. Rome is our point of departure, so if rent a vehicle need to start at one destination and return at another

Near Siena could mean a lot of things--you also mention Cinque Terre so I am still confused, but here is how I would work it out.
If it is a rural stay and you want to leave every day, then I would rent two cars--this is easier if yours is the kind of group that may want to do different things. That means at least two of you need IDPs, but it keeps one person from having the responsibility of driving a van (and parking it!). If you will be relaxing at an agriturismo most of the time, or will be close enough to a town with provisions, etc., then you probably don't need a car every day and could book a driver for a couple excursions.
If wine is going to be involved, then you need a driver--I would ask your accommodation host about this. It should be possible to have you all driven together in a van.
If you rent cars, you can drop them at Rome airport or a spot outside the ZTL, or pick a convenient location outside of Rome and take the train.

There are 6 of us traveling for 5 days from Cinque Terra area to Rome.
Staying near Siena and taking trips from there.

Sorry, threesibs, but we still need more info. Siena is not in the Cinque Terre area, and "near Siena" could be a rural farm or a very small town without train service or much, if anything, for public buses. Depending on location, you may not have much of a choice between renting a car or not if day-tripping is in the plan.

Where those day trips will be is also a factor: for instance, you don't want to drive into Florence due to many restrictions on where you can take the car. It can be gotten around by parking on the outskirts and taking public transit in but something to be aware of. Other Tuscan towns also have restrictions on where you can drive. Personally, I think the trains (and in some cases buses) are much less stressful but it depends on how much homework you want to do, where you intend to go and where you intend to stay. Some visitors rent just for a day to bump about the countryside.

Editing to add: Another excellent point from valadelphia about the wine/alcohol. European drink driving laws are generally very strict. Taking public transit allows us to indulge at whim without worrying about wheel.

Rent a car, best option by far.

As an example, Europcar lists minivans (supposedly to hold 7- 9) for about 500 euros for 5 days from Siena for a week this coming October.

You need to pick your routes/calendar/etc to get a handle on rental car costs versus trains for 5 people.

Driving is great way to see Tuscany and Umbria, but "least stress" is not compatible with driving in Florence or Rome. And, you can't drive in the Cinque Terra.

I would suggest mixing trains (CT to Florence) Car (Florence-Siena-Tuscany/Umbria) and back to train (to Rome).

Have fun!