The troops were killed on Wednesday at 7 pm (1600 GMT) in the area of Jabalia refugee camp in the northern Gaza Strip, the military said in a statement.
The latest fatalities take to 278 the number of Israeli troops killed in the Gaza military campaign since the start of the ground offensive on October 27.
"Five soldiers of the 202nd Paratrooper Battalion were killed last night in a mass casualty incident as a result of fire by our forces," the military statement said, adding that seven other troops were wounded.
Two tanks in the area, which has seen particularly fierce fighting in recent days, opened fire on a house used by the Israeli battalion's deputy commander, the military said.
"The shooting consisted of two tank shells," it added.
"From the initial investigation... it appears that the tank fighters, from the ultra-Orthodox paratrooper company Hetz, identified a gun barrel coming out of one of the windows in the building, and directed each other to shoot at the building," the statement said.
On December 12, the military said that more than a tenth of its troops killed in Gaza at that time died as a result of Israeli fire, while some other deaths were caused by accidents.
Fighting has raged in recent days in the northern Gaza Strip, with an army spokesman saying there were "attempts by Hamas to rebuild its military capabilities" months after Israel had declared the Palestinian armed group's command structure in the area dismantled.
Fierce battles and heavy Israeli bombardments have been reported in north Gaza's Jabalia refugee camp and the central Nuseirat camp since the army launched a "targeted" operation focusing on the southern city of Rafah in early May.
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