59...Kg6 and white can resign.
Need help with endgame, rook vs 3 connected pawns
45...Rb5 is a thematic move in this and similar positions. I wouldn't expect you to see it, but it's a good one to remember for the future.
And in general, you want the rook behind the pawns with your king in front.
Sometimes the rook is useful from the side, to give checks for example. In that case ideally your rook operates on one side of the pawns, and your king on the other so they don't get in eachother's way. Of course here that's not possible, but with pawns on center files for example.
Rook in front of the pawns is generally the worst choice. It will get in your king's way. The king could stay out of the way by going behind the pawns, but then the pawns just advance away from the king.
When choosing which pawn to place your rook behind, in general you'll want it behind the farther advanced pawn. Notice this limits two pawns at once. The pawn in back can't advance because it undefends the front pawn. The front pawn can't advance because it loses the protection of the back pawn.
I'm really bad at my endgame, we ended up in a similiar position with 3 pawns and 2 rooks each, however his pawn was one rank ahead of mine. Could someone point of my endgame mistakes and how to play connected pawns.