Chapter 5 - Begins at 24:31
in the video below.
You have to complete all four paths here to continue. For path I, you first need to flip all the tiles white-side up. To do this, step forward so that you're right up against the first row. Whenever a visible tile leaves your view, it will flip. Strafe left/right to flip the two side tiles so that they are the same as the center tile. When all 3 are blue-side up, step forward so that the entire first row leaves your view and you're looking at the second.
For the second row, you'll strafe left/right to flip the two side tiles white-side up to match the center. However, since they're correct already, when you step forward and row 2 leaves your view they'll flip blue side up. Simply step back just enough to see the full 2nd row, then step forward again to flip them all 3 back from blue to white.
Continue this process of strafing left/right then moving forward, etc so that each row is white-side up. When the final row flips, the door to the side will unlock.
Head inside and go to the end of the branch that has the line with an arrow at the end on the wall. Line yourself up mirroring it and walk across all the pressure plates in the floor so, starting with the 'beginning' of the line and ending at the arrow. This opens the door at the end of the blue/white tile floor hallway.
At the top of the stairs you'll face a circular floor puzzle.
*Painting Alert - This is painting # III for the secret achievement, just to your right when you enter this room. Keep this in mind when you return to view the 5 paintings in order.*
Spin the circles on the floor by walking on them so that the line/barrier in each lines up with the one in the center of the ring (the only one you can't spin by walking on it). Once all the lines are lined up, the mural on the circle will be complete and the next door opens.
The ramp puzzle in the following room is extremely difficult to describe. Check timestamp 30:39 in the walkthrough video to see what the completed room looks like from the entrance doorway. This should show you what you need to complete it. It's not hard, just hard to describe.
Once you head to the top of the ramp puzzle and view the dais with a 'I' in it on the floor, pathway I is complete. Head all the way back to the beginning and enter pathway II.
At the start of pathway II, use the levers to raise sections of the wall to create a staircase up out of the area. This is pretty simple but is shown in the video guide if you're struggling. In the next room, counting from left to right push buttons 1, 2, and 4 in the top row. The bottom row is buttons 3 and 4. Next just walk into the gazebo and look at the ceiling then spin in a circle to open the roof and allow light in to finish.
For pathway III, head around the spinning globes and push the switch when the three rotating clear globes are all at 90 degrees to the left, then look through all 3 at the light in the center.
For the next room, head behind the clear globe with a III at it's base and press right up against it, looking through it so you see 3 glowing orbs through it as well as 1 glowing orb through each of the other 3 clear ones. Following this just circle-strafe around the large silver globe to spin all its rings into place and complete pathway III.
For pathway IV, the raised pathway mimics the puzzle wall to your left as you enter. See timestamp 36:15 in the video for the solution. Complete the puzzle and walk across the raised walkway, going backwards up the stairs around the pillar in the next room lest they retract into the wall if you try to walk forward.
Head back out and through the main door, onto the dais to complete the chapter and unlock Forks In The Path.