Two Islamic Jihad leaders died and three civilians, one of them a tunnel smuggler, Palestinian medics said.
Meanwhile, Gaza militants have fired 19 rockets and mortar shells into southern Israel since Wednesday, the army said.
The attacks threaten an informal truce agreed by Israel and Hamas on Sunday after days of escalating violence.
The informal ceasefire was called in an attempt to halt rising tensions, following a series of shooting attacks near Eilat last Thursday, which killed eight Israelis.
In the following days, Israeli air raids on Gaza killed 15 people, and more than 100 rockets and mortar shells were fired from Gaza at Israeli towns and cities, killing one man.
Many more were wounded on both sides. more