They say the gunman was a former employee at a store on the estate who was sacked in April. He took his own life after the killings.
There is no suggestion the killer was a member of a subversive or terrorist organisation, police say.
The shooting came a week before the first anniversary of the Pulse nightclub shooting in the city.
Forty-nine people were killed in that incident.
'Workplace violence'
Orange County Sheriff Jerry Demings said police had arrived at the scene of the shooting to find four people dead. A fifth employee died while being taken to hospital.