Please see my reply to the post below on this subject:
https://community.ricksteves.com/travel-forum/italy/smart-phone-advice-for-solo-traveler
There are 4 major cell phone providers in Italy: TIM, Vodafone, Wind, 3.
The last two just announced a merger, after which they will become the largest provider.
Each has their own stores, plus there are numerous authorized electronic stores that can provide you with everything you need for your Iphone5 (I also have the same model, unlocked, which I use every year with an Italian SIM card). You can find the location of their stores/authorized dealers in their websites. Just search: "Trova Negozio" (=find store") then zoom in the city where you intend to buy it (I presume the city where you first arrive.
The store staff will put the SIM card in for you if you wish, or you can very easily do it yourself using a paper clip.
The SIM card will include data. Go to the above linked post and I posted there two offers for foreign tourists by both Vodafone and TIM. They are the best deal for you as they include minutes to call overseas back to the US. They also include at least 2Gb of data which is plenty. The cost is €30, all inclusive.
You can also buy a cheap dumb phone in Italy or even in the US (make sure it's a GSM Quad Band unlocked phone). I'm not sure if they sell SIM card with no data nowadays. But in your case, since you already have an unlocked Iphone, just use that one. The cost of a cheap phone is still at least 30 euro. With the same amount you can buy a SIM card with the data plan I mentioned above for your Iphone.