The military had stepped up deployments in the northern city after one person was killed on Wednesday night, carrying out raids and seizing weapons.
"During their operations the forces were fired upon, which led to the martyrdom of one soldier and the wounding of several others," the military said in a statement.
It was unclear where the soldier was killed, but the security official said the four others killed overnight in shootouts and sniper fire were killed in the Sunni neighbourhoods of Bab el-Tebbaneh and Qubbeh.
The source said 26 others were wounded overnight, including six soldiers, adding that civilian residents of the area were fleeing sporadic gunbattles throughout the night.
On Wednesday, a sniper shot dead one person in Bab el-Tebbaneh, according to a security official, who said four others were wounded in an exchange of gunfire that followed.
Bab el-Tebbaneh borders the Alawite Jabal Mohsen area, and gunmen in the two areas regularly open fire on each other.