The air force destroyed 29 hideouts, 97 cars, and several explosive devices that the militants prepared for attacking the security forces, the army said in a statement.
Some 158 criminal and wanted elements were arrested during the raids, it added.
During the shoot-outs, two officers and three soldiers were killed and four security men were wounded, the statement added.
Egypt has been suffering a wave of terrorist attacks that have killed hundreds of policemen and soldiers following the military removal of former Islamist President Mohamed Morsi in July 2013.
The terror attacks had been centered in the restive North Sinai before spreading to several provinces including the capital Cairo and starting to target the Coptic minority via church bombings.
Most of the attacks were claimed by the so-called Wilayat Sinai, a Sinai-based militant group affiliated with the Islamic State.