Now you need to reach the west side of the cavern. (The Survival Instinct beacon shows where to go if you have it enabled in the Options > Gameplay menu.) Start by jumping onto the sixth bell.
It begins to sink, causing the the seventh bell to rise, but before it can move all the way up, it gets stuck on a mass of debris jutting out from the ledge. Jump from the sixth bell to the craggy wall ahead. Climb to the top.
As soon as you pull up onto the ledge, look up to spot the last whistle (5/5). Shoot it down to complete the Whistle In the Dark Challenge for an XP bonus.
Now for phase two of the puzzle: Move to the top of the slope, cracking open a salvage crate along the way
Stand next to the winch and press Interact to use your climbing axe as a handle.
Rotate the left stick or press A/D to turn the winch, causing the wooden turntable below to rotate. You only need to rotate it a quarter turn, so the tracks along the middle line up left to right, as shown above.
Release the winch and head up the slope to the left of the turntable to find another wooden cart.
Approach the cart from behind, grab it, and push it forward down the slope.
If you rotated the turntable correctly, the cart should roll onto it and stop in the middle. (If the cart does not roll onto the turntable, go back to the winch, adjust the turntable as needed, and then push the cart into position.)
Return to the winch and rotate it a quarter-turn counterclockwise, so the rope-wrapped handle on the cart faces Lara.
Let go of the winch and shoot a rope arrow into the handle of the cart. As long as Lara is standing close to the winch, she should anchor the other end of the rope to the winch's spool.
Now crank the winch to pull the cart up the slope toward you.
Let go of the winch, move close to the rope line, and press Melee to cut it, sending the cart barreling down the hill into the pile of debris.
This frees the two bells so you can move forward. You also receive a nice XP award for solving the puzzle.
The sixth bell is now higher than the seventh one. So move up the slope on the right...
...and jump onto the sixth bell. Quickly, before it can sink too far, jump to grab the ladder dangling from the ledge ahead. Climb to the top.
Move forward, loot another supply canister, and climb the stairs to the right.
Scramble up the stone slab to grab the handhold above. Climb around to the right.
BUG NOTE: Apparently in the PS4 version, the stone slab in the screenshot above may be missing. In that case, you'll need to jump out and grapple the ledge above by pressing Square. Then climb up the cable to grab the ledge.
As Lara nears the gap in the ledge, a flock of bats flies out, causing her to lose her grip. Quickly press Interact to recover.
Continue climbing to the right, then downward along the craggy wall. Rappel down toward the altar to trigger a cutscene.