This message is to the Travel Advisers to this board.
When giving advice to individuals who want to travel to the Cinque Terre from Florence via train, be aware of an another option introduced for this Jubilee year. It's a FrecciaBianca from Rome to Genova (and back) passing through Florence (Firenze Campo di Marte). That is probably the fastest option from Florence to the Cinque Terre for a day trip (or for any trip).
FrecciaBianca 9758
Firenze CM: departs at 7:38
La Spezia C: arrives at 9:11
FrecciaBianca 9787
La Spezia C.: departs at 20:06
Firenze CM: arrives at 21:40