Four of the rebels were killed in fighting in a mountainous area in the province of Sirnak, where security forces had last week launched an operation against the outlawed Kurdistan Workers' Party (PKK), now known as KONGRA-GEL.
The soldiers also seized a "large number" of weapons and discovered food supplies in caves used by the rebels, Anatolia said on Friday, adding that the operation in the region was continuing.
A fifth rebel was killed on Thursday night in a clash in a rural area in the nearby province of Diyarbakir, Anatolia said.
The PKK, which has waged a 15-year war for self-rule in the mainly Kurdish eastern and south-easterns regions of Turkey, called off a five-year unilateral ceasefire with Ankara on 1 June.
Since then, the group has been blamed for a series of deadly attacks on security forces and the bombings in August of two hotels in Istanbul, in which two people were killed.