The tragedy comes after 18 deaths were reported when emergency airdrops landed in Gaza earlier this week and riots ensued.
According to the aid organization Red Crescent, three of the five dead must have been shot.
On Saturday, thousands of people had gathered at a roundabout in Gaza City before 15 trucks of flour and other food were to be distributed.
According to eyewitnesses, a commotion broke out at the scene. Gazans who were monitoring the aid delivery are said to have fired shots in the air, Israeli troops are also said to have opened fire while some trucks ran over people trying to get the food.
The Israeli military says it “has no information about the described incident”.