Well, to surmise. Scarapawn got it right, and provided the winning variation. 
When I posted my 'intuition', I resorted more or less to general rules,
as I had no board available at the time. I actually calculated scarapawn's variation but mistakenly thought that black had even some drawing chances there, seeing that white at least couldnt count on a win he tried to keep his king in the neighborhood of the h-pawn (because of black's rank checks). But with the position on the board it is easy to see that white wins hiding his king on g7 or f7.
Thx scarapawn!

White is a pawn up, he has the most active king, c7 is weak. Using Marin's general rule white is at least two points up-white must be winning (which confirms my first impression).

I concluded with similar variations as already presented by sacapawn.

I have deep respect for micawbers endgame skills - so maybe I am wrong?

Of course we need general rules. We are not computers. Can't always calulate till the end. Need some guidance to look for possible defencive ideas before converting it into pure variations.

This is intersting indeed, esp. the a-&h- pawns vs. no pawns for Black.

But I must admit I am confused with Micawber's point (b) above. I thought Black would have had more drawing chances if White actually plays b6 instead of a6. Then with White pawns on a5&b6 and a Black King on a6 it seems easier to hold the draw with an activated, checking Rook.

??

I recently won an endgame as White in this position:

W: Kc5, Rh8, a5, b5, h4

B: Ka7, Rg4, c7, g6

White to play.


I guess it shows that I need to work on my endgames, but I had some real trouble with this, and thought that the position might actually be drawn before falling on the right continuation (which may--or may not--have been aided by my opponent).  I'd be happy to show the following moves, but is this game drawn, or do White's connected pawns (and pawns on either side of the board) ensure a White victory?