The first parked car was found aflame at 3 a.m. Saturday in the 200 block of California Street in the city's Financial District.
The second was at 11:40 p.m. Saturday at Franklin and Fern streets and another fire was reported at 4 a.m. Sunday at Olive Street and Van Ness Avenue. Both of those locations are in the Western Addition neighborhood.
A fourth vehicle burned at about 2:30 a.m. today in the 100 block of 12th Street, in the South of Market neighborhood.
Details about the fifth arson fire were not immediately available, spokeswoman Sgt. Lyn Tomioka said.
An arson investigator hasn't determined that the blazes are related, "but hasn't ruled that out," Tomioka said.
No arrests have been made and no suspect information was available. Anyone with information is asked to contact the Police Department's anonymous tip line at (415) 575-4444.