marc,
Could you clarify "firenze rediredi airport"? Are you referring to travel from the C.T. to Firenze Rifredi station to FLR (Peretola) airport?
As the others have mentioned, it's an easy trip from the Cinque Terre to Florence. There's always the chance of a "disruption" caused by a strike or whatever, but those are announced in advance so you'll have lots of warning. Also, you'll probably to warned by the locals that a strike is forthcoming.
Which of the five towns are you staying in? That will have a slight bearing on transportation towns. The quickest route would likely be train to Firenze SMN and then Taxi to the airport (I wouldn't bother with Buses). The fare is "fixed" (higher for those with lots of heavy luggage) and it's a short trip since the airport is relatively close to town (depending on traffic of course).