LOS ANGELES (AFP) - The death toll from a mass shooting in California rose to five on Sunday after a 26-year-old woman seriously wounded during the gun rampage died in hospital, authorities said.

Marcela Franco was caught in a hail of bullets that also claimed the life of her father Carlos during the shooting on Friday in the upmarket beach resort of Santa Monica carried out by a gunman clad in black and wearing body armor.

Local media reports have identified the gunman as John Zawahri, who was due to turn 24 on Saturday. The gunman was shot and killed by police after being cornered in the library of Santa Monica College.

Marcela Franco and her father, a groundskeeper at the school, died after Zawahri opened fire on a car they were traveling in at the college on Friday.

"I am saddened to report that Marcela Franco passed away this morning at Ronald Reagan UCLA Medical Center," Santa Monica College president Chui Tsang said in a statement on the school's website.

"Her family was with her by her side. Marcela had registered to attend classes this summer at SMC and was with her father Carlos when Friday's tragedy struck.

"Our deepest sympathies go to the Franco family. At an appropriate time, the college will convene a campus-wide memorial." Police have still not pinpointed a motive for the killings. The carnage began on Friday when a house was set on fire in Santa Monica. Police later found the bodies of Zawahri's father and brother inside.

The heavily armed gunman, carrying some 1,300 rounds of ammunition, then headed to Santa Monica College, where he fired indiscriminately at students before eventually being shot dead by police.