After retrieving secret #5 and using the rope to swing over to the elevated walkway on the east side of the room (as shown in the previous section)....

Follow the elevated walkway toward the pole.

Turn around and shoot the 2 bats that drop down from the ceiling behind you.

Then take a running jump to the base of the pole.

Climb the pole until Lara is hanging just above the jutting ledge. Then rotate around the pole so the ledge is behind her...

...and jump back to land there.

Shoot another bat. (If it doesn't appear right away, just keep going. It'll turn up eventually.)

Turn left and take a standing jump to grab the black switch. This raises the hinged ledge behind you.

After pulling the switch, Lara falls to the ledge below. Draw pistols and kill another bat.

Take a standing jump to the base of the pole, climb up...

...and backflip onto the jutting ledge as you did before.

NOTE: You can jump directly from the pole to the hinged ledge, but getting the proper angle is tricky.

Jump onto the hinged ledge...

...and reach into the niche to get a wooden TORCH.

Now you need to get back down to the floor. Lara won't climb while holding the torch, so press the Draw/Holster Weapon button to throw it down first. Try and notice where the torch lands since you'll need to retrieve it.

Take a standing jump to grab the pole, slide down, and let go. Then take a standing jump with Action from the base of the pole into the wide opening.

Pass under the arch and move to either edge of the elevated walkway. Take a standing jump to grab the ledge near the wall. Then drop to the floor, taking no damage.

[Tomb of Semerkhet Walkthrough]