Braid

World 5 is the fourth world you'll have access to in the game. I actually found the 5th world easier than the 4th, you control a shadow of yourself who does basically whatever you do when you rewind time. Once you finish all the levels you'll unlock the achievement.

There are 7 levels with a total of 12 puzzle pieces.
The Pit (1 Puzzle Piece)
So Distant (2 Puzzle Pieces)
[Unnamed] (2 Puzzle Pieces)
Crossing the Gap (3 Puzzle Pieces)
Window of Opportunity (2 Puzzle Pieces)
Lair (1 Puzzle Piece)
Fragile Companion (1 Puzzle Piece)

See the achievement "Solved World 5" for help on completing the level/getting all puzzle pieces.