"There were three raids today (Tuesday)... targeting a food depot, a chemical goods factory and a small port," the Zuara official told AFP.
He said seven people were killed, including the five Africans, and 25 wounded, a toll that could not immediately be confirmed.
Forces loyal to former general Khalifa Haftar, who is allied to Libya's internationally recognised government and has vowed to expel Islamist militias from main cities, carried out the raids, the official said.
The warplane that launched the raids had taken off from an air base in Al-Woutia, also in western Libya, that is controlled by factions loyal to Haftar.
In Benghazi, meanwhile, four people were killed and seven wounded when a rocket crashed into the centre of the eastern city, a medical source said.
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A military official said the rocket had been aimed at the Al-Jala hospital that treats soldiers and Haftar's forces, but that it missed its target.
More than three years after dictator Moamer Kadhafi was toppled and killed in a NATO-backed revolt, Libya is awash with weapons and powerful militias, and has rival governments and parliaments.
Last week, Haftar gave himself two weeks to take Benghazi and three months to recapture the capital Tripoli.
The former general has been battling Islamist militias who took control of the country's biggest cities this summer after their defeat in elections.
Forces loyal to Haftar and Prime Minister Abdullah al-Thani are fighting for control of Benghazi and have also launched an offensive west of the capital.
"For Tripoli we are only at the beginning," Haftar told the Italian daily Corriere della Sera. "I have given myself three months, but maybe we will need less."