For convenience, here is the original screenshot showing the numbered sequence for moving the hook along the tracks. When Lara climbs up the ladder to the rafters, the hook is at position 5.

Crawl to the right and press Melee in time with the on-screen prompts to kick the pipe out of the way. When the pipe shifts, so does the grate Lara is sitting on, and she drops back down into the room below.

Turn right and move under the hook and into the corner.

Turn around to face the hook (and the room where Alex is trapped). Use the rope ascender again to pull the hook toward you (6).

Move under the hook and turn to face it. Then jump onto the ladder...

... to push the hook back toward the entrance (7), which is the same as the starting postion (1).

Now move back toward the stairs near Alex.

Turn around and pull the hook toward the door with the live wires once more (8).

Now that the pipe is out of the way, the hook can reach the door and attach to the wires.

This brief cut scene shows you've done it right.

Move back to the entrance and use the rope ascender one more time to pull the hook away from the door (9), breaking the wires so you can get in.

You receive 100 XP and a new goal.