The publication left open the question of how they had died, with chief military spokesperson Rear Admiral Daniel Hagari saying post-mortems were pending.
"We will brief the families and then, depending on what they approve, the public," he said on Sunday.
The three soldiers and two civilians were among 240 people dragged back to the Gaza Strip by Hamas gunmen during the cross-border rampage of October 7 that sparked the war.
The military announced the repatriation of their bodies earlier this month.
Hamas last week published video showing three of the hostages alive in what appeared to be a narrow, white-tiled and windowless bedroom with an electric wall socket.
In a Hebrew chyron directed at Israel, the Iranian-backed Islamist group said: "Your military weapons killed the three."
Hamas has previously said some hostages died in Israel's shelling of Gaza.
It has also threatened to execute hostages.
Sunday's military publication came as Prime Minister Benjamin Netanyahu said Israel would deepen operations in an almost 12-week-old war whose toll on Gaza civilians has alarmed Western powers also worried about the 129 remaining hostages.
Video released by the military showed its engineers in a dark and dusty tunnel network which, it said, had two storeys - one 10 metres down and the other "dozens of metres" deeper.
One tunnel ran to the home of Ahmad Al Ghandour, chief of Hamas' North Gaza brigade, the Israeli military said.
Hamas declared him and several other commanders killed in action on November 26.
Israel said they were targets of one of its airstrikes.
The video showed a section of a tunnel lined with white tiles, as well as a similarly designed bathroom with a basic shower, toilet and sink, and a workroom with a corner table and bench.
One tunnel had a drinking water dispenser and a pile of bullets.
The military video did not include images corresponding to the hostages' bedroom shown in the Hamas video, whose ceiling appeared differently designed though also tiled in white.
