This sequence is also shown in a gameplay video.
Stand on the raised area in the corner of the room with the alcove containing the silver reward behind Lara to the right and the entrance and tunnel ahead on her left, as shown above. Face the left horizontal "arm" of the rack straight ahead and take a running jump to grab it.
Momentum pivots the rack 90 degrees clockwise.
Now you're facing the center rack. Swing around and jump to grab the bar on the center rack, which then turns 90 degrees counterclockwise.
Swing and jump to the next rack, which turns 90 degrees clockwise.
Now you're facing the wall below the exit. Swing, jump and grab the narrow, horizontal ledge running the length of the wall. Traverse to the right as far as you can.
Jump past the rough area of wall to grab on where the narrow ledge continues.
Climb to the right a little more until the grabbable arm of the nearest coat rack is directly behind Lara, as shown above. Lean away from the wall and jump to grab onto the rack. Release the direction controls and let the rack pivot toward the alcove with the reward.
Swing around the bar and jump to grab the edge of the alcove. Pull up and take the silver reward (5/5)
[Part 2 | Return to the Bolivia Walkthrough]