Go on trenitalia.com and switch to the English version. Put Monterosso and Orvieto in the From/To Fields and pick a time of travel in the early morning from the drop-down menu. Click search.
On the next page, use the drop-down menu to sort the search results by time of travel. The fastest route takes 5 hours, departing from Monterosso at 15:12. Two changes.
Did you check if Flixbus runs buses between the Cinque Terre (or La Spezia) and Florence?
Ignore the above post, some would rather give misleading info for years than admit they have been wrong for years.
Trenitalia has uploaded the schedules up to June 8, 2025. They could add some slow local trains between the 5 villages in the Cinque Terre after Easter Monday if the local government pays for them, but the idea of fast, long distance day-trains being available only 1 month in advance... it's just wrong.