A group of radical Kurdish militants also claimed responsibility for a bomb attack against an office of the ruling Justice and Development Party (AKP) in Istanbul in what it described as a reprisal attack for the unrest.
Two of the slain soldiers died while on patrol in the mountains of Sirnak province near Iraq when they stepped on a landmine planted by militants of the rebel Kurdistan Workers' Party (PKK).
Three others were shot dead in an ambush as security forces launched a search operation in the area to hunt down those responsible for the mine attack.
Two PKK militants "were rendered ineffective" in the ensuing clash, without specifying whether they were killed or captured.
Separately, a policeman died from his injuries after PKK rebels opened fire with automatic weapons on a police station in the town of Genc, Bingol province.
More than 37,000 people have been killed since 1984, when the PKK, considered a terrorist group by Turkey, the United States and the European Union, took up arms for self-rule in mainly Kurdish southeast Turkey.
The latest deaths followed a week of violence that claimed 15 lives as
Kurdish rioters clashed with security forces in the southeast and in Istanbul, in the worst urban unrest in the country for years.
Police opened fire to disperse the demonstrators, many of them teenagers and children, who torched banks and public buildings, vandalized shops and threw Molotov cocktails.
The victims included three women killed on Sunday in Istanbul when a petrol bomb attack set a bus on fire, causing it to crash into another vehicle.