Four people from the same family were found dead in a flooded house in the city, where 40 centimetres (one foot, 4 inches) of rainfall in four hours transformed streets into rivers and washed away cars.
The Corriere della Sera daily said the dead were a little girl, her parents and a grandparent.
A fifth body was found in an area devastated by landslides. Three other people were missing, the fire brigade said.
Italy's civil protection service issued a code orange alert for Florence as the storms, which began in northern Italy overnight, swept down the country towards the south.
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Underpasses were being closed as a precaution in the capital Rome.
Coldiretti, Italy's main agricultural organisation, said the bad weather was aggravated by coming hard on the heels of a drought which had left the land drier than usual and unable to soak up the rains.
Rainfall in Tuscany in particular had been down 57 percent this summer, it said.
It put the cost of the damage at over 14 billion euros (USD 16.8 billion) in the last 10 years.