A very good study. I have seen this before and it is a reminder of the imporatnce of understanding King & Pawn engames. Many players understand the importance of the opposition, but forget that it is a means to an end not the end of itself. Opposition is meaningless if the defending King cannot drop back, and this is the case with a pawn on the fifth rank.
Knowing the opposition rule(s) can help!

Thanks for the input. I learnt some here. I learnt the hard way that opposition does work on the 6th rank few months ago. Thanks again.
BTW i don't think the first move is important here. In my humble opinion, we can juggle the first 2 moves. The 3rd move is the KEY move for me. Correct me if i am wrong.
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Thanks for showing how wrong i was. Appreciate it. :)

"i don't think the first move is important here. In my humble opinion, we can juggle the first 2 moves. The 3rd move is the KEY move for me. Correct me if i am wrong."
Of course, the first move is important! Please look under solution(move list). The immediate b5! is necessary to fix the black pawn on the six row. Otherwise after 1. Ke4 b5! it will be the opposition on the fifth row=draw

Many players understand the importance of the opposition, but forget that it is a means to an end not the end of itself.
My experience as well. They know about the endgame theme "opposition" but that doesn't mean they know the correct king paths / triangulation maneuvers.

Sir,It is said in the annotations of the move list that the king should go in to a diagonal opposition ! I just want to know the reason ,why ?
Also,if that is the rule then after 2.Ke4,the King should have moved to 3.Kd5 instead of 3.Kd5 ,isn't it ?

Why does 6. Kd7 not work (I played this and can't see why it doesn't win in the same way as 6. Kd6)?

Grigoriev was a great endgame composer - I like practical compositions like this one a lot. For more info on opposition read this:
https://en.wikipedia.org/wiki/Opposition_(chess)
More K+P vs K+P endings can be found here, inc 3 by Grigoriev:
http://www.chess.com/blog/post?id=95948

Amalangi, King opposition is mainly a method to stop the advance of the opponent king. So, if you want to get into opponent`s area with your king, and opponent`s king wants to stop it, you have to take yourself the opposition with your king.
At that point your opponent would like to pass, but he has to make a move! So often he has to make a move with his king and your king can come forward.
The direct, the diagonal, the far distant opposition work normally after that described method
binblaster, of course you are right!

Why does 6. Kd7 not work (I played this and can't see why it doesn't win in the same way as 6. Kd6)?
I agree, played this too - does 6. Kd7 not work? (Edit: ignore this, just read mauerblume's latest post!)
BTW Black to play in the original position draws by playing 1...b5, then keeping his King on a8/b8/c8 etc so that when White plays Kxb5 he can reply Kb7.

Amalangi, King opposition is mainly a method to stop the advance of the opponent king. So, if you want to get into opponent`s area with your king, and opponent`s king wants to stop it, you have to take yourself the opposition with your king.
At that point your opponent would like to pass, but he has to make a move! So often he has to make a move with his king and your king can come forward.
The direct, the diagonal, the far distant opposition work normally after that described method
binblaster, of course you are right!
Thanks ,Sir !Got it now !:-)

Idea behind this study is that wPb5/bPb6 wins for white, but wPb4/bPb5 is a draw (in another way, K+P v K is a draw with white K directly in front of the pawn and no opposition, except with his K on the 6th rank), as well as the basic idea of opposition.
Annotated analysis!
Read it all for it to be useful. Understand the basics of K+P v K and K+P v K+P.
It also helps to know the critical squares, or squares in relation to the pawn that if the king reaches, he automatically wins. I was able to solve it because knowing that the key sqaures of a pawn double when they pass into the enemy's side of the board playing b5 first was intuitive.

It also helps to know the critical squares, or squares in relation to the pawn that if the king reaches, he automatically wins. I was able to solve it because knowing that the key sqaures of a pawn double when they pass into the enemy's side of the board playing b5 first was intuitive.
This is the correct way to think about this puzzle imo.
The key squares are much more basic concept than the opposition because opposition only makes sense when fighting about certain key squares.
Please look at the following study:
So, what do you think? Is it a draw or a winning position? Well it is a winning postion, but only if you find the correct first move! A Tipp: The knowledge of the "Opposition rule(s)" can help
The variations and my comments you can see later under solution (move list)