Ciao Leslie,
Sounds like a great trip as a celebration for your mom, you will all really love Italy and Tuscany!
As far as day tours, are you thinking of something you can do on your own just using trains and buses or an organized tour you can join in?
If you're planning to do organized tours, either Florence or Siena are great bases because many tours depart from the two towns - you can get an idea of what is offered (lots!) in
general here and here for those that specifically
start from Siena.
If you don't have a car and want to do wine tastings, then I highly suggest the organized tours because the wine areas are hard to reach with public transportation.... and even when you have a car, they are still a good idea so that you can drink up and enjoy more freely without worrying about driving LOL

The tours are also great if you want to visit some of the areas further away from Florence that are hard to reach by bus or train, such as the Val d'Orcia/southern Tuscany where you can find Montalcino and Montepulciano.
If instead you want to do a few days trips on your own, then if you use Florence as your base you can easily go to
Pisa and Arezzo by train and to Siena by bus and to San Gimignano with a combination of train and bus (train to Poggibonsi, bus the rest of the way).
If you want to visit the area to the south of Siena, then you could also split up your 5 days into 3 in Florence, 2 days in Siena and that way have less travel time for those other days.
Definitely spend an entire day in
Siena - many don't, but I really like it and feel there is enough to see between the monuments in Piazza Duomo and Piazza del Campo to merit a full day.