The incident happened at about 1:20 a.m. at the Den Bar & Grill on the 11400 block of South Hawthorne Boulevard.
A witness said an argument started inside the bar and spilled out onto the street; one man left and returned with a gun.
All of the victims were transported to an area hospital, where one man was pronounced dead. The four injured victims are expected to survive their wounds.
Several people were taken into custody after getting into confrontations with police. Los Angeles County sheriff's detectives and Hawthorne police are investigating the motive, but they said it appears to be gang-related.
Police are still searching for the gunman. If you have any information you're urged to contact the Los Angeles County Sheriff's Department's Homicide Bureau at (323) 890-5500.