Rome to Florence

That will put you pretty late into Florence. Would you consider a night in Rome? With a 5.30 (1730) landing I assume it is not an international flight so you can directly leave the airport. With four people and assuming min luggage I would grab a cab to Termini - train station. Buy a ticket on the next high speed train to Florence. With luck you can catch a train around 7.30 (1930) which puts you in Florence by 10 (2200). Worse case, maybe an hour later.

The last fast train leaves the airport at 1857 and arrives in Florence SMN at 2122 (change trains in Roma Tiburtina). You may be able to catch this train depending on where you are flying into Rome from. If you have to clear immigration, you might not make it. Here is a link with some options.

https://www.lefrecce.it/B2CWeb/search.do?parameter=searchOutputViewer&cFID=gKXrE2xTYMsa

You might also want to check into a flight from Rome to Florence at skyscanner.net.

Actually, unless you have a major delayed arrival, you should make it to Florence on the same day. The last available departure departs from the airport train station (Fiumicino Aeroporto) at 7:57pm.

Regionale 22111: Dep 19:57 from Fiumicino Aeroporto > Arrives Roma Tiburtina at 20:45
FrecciaRossa 9564: Dep 21:00 From Roma Tiburtina > Arrives Firenze S. M. Novella at 22:35

Base (full fare) Price 52.00 €.

Flights options are limited. Only 3 flights a day from Rome to Florence, with Alitalia (in code share with Delta if you are interested):
Flight Departures are at:
10:25
14:55
21:50
So you should be able to make the last one.

Just did this same shuffle. Some lessons learned:
- The walk to the Leonardo Express is LONG.
- With 4 people, the relative cost of a car/cab is much more competitive and efficient than taking the train to Termini. Cabs are plentiful and won't waste time getting you to Termini
- Do not try to use Uber at FCO unless you have a data plan and phone number that'll have you connected and that an Italian driver can/will call.
- As tempting as the advance fares are, don't purchase your train ticket from Termini to SMN in advance. If you're delayed, you'll eat those tickets.

Not knowing your budget or preferences, I can suggest a bus if you feel the train times will rush you. There is a MegaBus that leaves Tirbutina at about 830pm and arrives in Florence (at a bus stop near SMN) around midnight. That might buy you some extra time.

How you get to whichever Rome station is up to you. But since the last Frecciarossa from Tiburtina departs at 2100, I think you should have enough time to make that one unless your plane is very delayed.