Ciao and happy anniversary! A wonderful way to celebrate
Well..... if you want one single place for those 5-7 days, I would recommend booking ahead.
If you're looking to stay in 2 or 3 places over those days, then you can wing it and book once you're here.
Also consider: what type of lodging do you want?
May is not yet high season across Tuscany but there are some types of lodging that rent by the week, not by the night.
Apartments in villas or farmhouses often rent by the week. Hotels and B&Bs by nights. So if you want the first, book ahead and have 1 base. If you want more than one base, not minding moving around, then you can go to hotels and B&Bs. It all just depends on what you prefer, and where you want to go.
You could book 2 places, one in southern part of Tuscany (you didn't mention, will you have your own car?) and another closer to Florence. That way less driving around once you're doing day trips.
I personally hate moving around too much every few days, but since you're already doing Amalfi and Rome with one base in each, you might also prefer to not move around too much.
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