The devices, which reduce poisonous gas emission from the exhaust system, have a high scrap value because of their platinum content.
They can cost upwards of £250 to replace but thieves also cause hundreds of pounds worth of damage in removing them.
An Avon & Somerset police spokesman said: “There have been five catalytic convertor thefts reported in the past two days in Keynsham. They are from vehicles parked on drives or outside houses and police believe they are connected.
“Investigations are under way and officers are appealing for anyone who saw or heard anything suspicious to call us on 101. “
The cars involved at two Toyota Hiluxes, two Citroen Picassos and one Kia Sportage.
Catalytic converters were originally just bolted on to the system, making them relatively easy to remove. On many cars now they are welded in place but, as was the case in at least three of the thefts, the perpetrators used chain cutters.
Last year a series of thefts from commercial vans parked in depots overnight in South Gloucestershire was thought to be the work of organised gangs.