Where are the secret levels on Reed?

After completion, Reed has five secret achievements which apparently correspond to five hidden levels.

In order of increasing spolieryness:

• is there any hint or marker for where a secret level may be in-game?
• which regular levels contain hidden levels?
• where exactly are the entrances to the hidden levels?

Solution 1:

“The game has 5 secret levels, for each level is given achievement” — @PXLink Twitter

There are no indications of where they are located, and it is impossible to re-enter a secret level (unless you clear your saved game progress).

To enter such secret locations, just jump into the right spot.

• 8, above the moving platform, at the ceiling of the pyramid-shaped area (Secret letter "R"!)
• 19, at the bottom right (Secret letter "E"!)
• 27, at the top middle, to the right of the middle saw, but only works if you have not touched the cube (Secret letter "E"!)
• 40, near the NPC (Secret letter "D"!)
• 47, near the NPC (Secret word "REEDIUM"!)

Solution 2:

The correct locations of all five entries is given in the accepted answer. But I'd like to add that there actually ARE indications about entries. See the screenshots taken from L19 and L40. There's a really subtle glowing dark light (animated) at the entry. It disappears after you enter it once.

The first image is taken from L19 and the second image is taken from L40. The other three are really hard to notice with bare eyes.

I can also confirm that the requirement "before touching the cube" applies to all five levels, not just L27. In any level if you touch the cube first, the entry will disappear even if you haven't entered it.