Mission 1: Baku
Weapon 1: M39 EMR
Once you reach the first open courtyard and take out the enemies that appear, drop down to the lower level and then cross over the other side. Climb up the broken rubble to second floor and in an open locker lying on its side will be the weapon.
Weapon 2: MG4
Once you reach the construction site and cross the road, go to the right side and enter the concrete cylinders located there. Inside the first one on the right side will be the weapon lying on the ground.
Weapon 3: CBJ-MS
Once you go through the tunnel to get to the second section of the construction site, go to the stairs on the right and cross the catwalk to the first set of pipes on the left. Hop over the railing and take a few steps to find the weapon sitting there.
Mission 2: Shanghai
Weapon 4: QBS-09
Once you exit the elevator, go around the corner and enter the door on the left. In the small room here, there will be a set of lockers on the left with the weapon leaning against them.
Weapon 5: RFB
When you exit the elevator after the rooftop fight and reach the large room with the large lion statue, look under the legs of the statue to find the weapon lying there.