If you don't want the save/power-up crystal on the ledge above the passageway, just continue through the passageway to get back to the room with the big, hollow tree. Skip the next 4 screenshots.
If you do want the crystal, carefully position Lara just before the step up into the passageway, in the right corner of the spike field, where there's a clear spot. Then jump straight up to grab the ledge above. If you don't grab on the first try and Lara drops back down into the spikes, she should be OK as long as she lands in this corner.
Pull up, get the crystal, and then follow the ledge to the left.
Step out onto the triangular tile at the end of the ledge.
Then slide down into the room with the hollow tree trunk.
Walk to the edge of the hole in the floor above the spikes facing the open end of the hollow tree. Then take a standing jump forward to grab the edge of the opening.
Pull up and crawl inside. This is SECRET #5. Crawl forward and pick up some flares and MP5 clips.
To get down, back up to the opening and hang from the edge above the spikes surrounded by angled blocks. Then hold Action and Back so Lara lowers herself and hangs from the edge above the spikes surrounded by angled blocks. Drop down onto the first angled block and hold Jump and either Left or Right.
Lara will hop back and forth between the angled blocks...
...until she reaches a corner and jumps out to the safe area. There are 2 sets of Desert Eagle clips on ledges at the back of this room. If you didn't already kill the tiger that came in when you opened the gate, you might want to climb onto one of the ledges with the ammo and shoot the cat from there.
There's also a flat, green rock to the right of the steps (when facing the gate) from which Lara can shoot at the tiger without being mauled.
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