Catherine

Stage 5 is The Quadrangle; it has three levels and introduces ice blocks. If you want a proper walkthrough, go here for videos:
http://catherinethegame.wikia.com/wiki/Walkthrough:Quadrangl...
http://catherinethegame.wikia.com/wiki/Walkthrough:Quadrangl...
http://catherinethegame.wikia.com/wiki/Walkthrough:Quadrangl...

If you'd rather get through the levels yourself, here are some tips for dealing with ice blocks:
You can jump up onto or off from ice blocks normally, but if you walk from another block onto an ice block you will slip and slide off the other side. You cannot hang from an ice block if you slide off of one this way, so it's easy to fall to your death if you aren't careful.
You can hang from ice blocks with no problem, though. If you jump up onto a row of ice blocks, jump down and hang from the edge of one and wall climb around to the block you want to get to.
If you push a block over an ice block, or push an ice block over any block, it will continue sliding until it passes the last block in the row. It will attach by the edge to the end of the row. However, you can pull ice blocks (or any block over an ice block) with no sliding.
TL;DR Be careful walking over ice blocks, hang from them or pull a block across them instead.

You can easily get the at the beginning of 5-1 by pulling an ice block out from the bottom to the corner of the landing and pushing it to the side across the landing.