5r1k/2p3pP/3p1P2/3PP3/p7/P2K4/6P1/2B5 w - - 0 1
The king can be checked (perpetual check) if it moves onto c4 and after that onto d4.
Is that really true, Alena? Compare the two solutions you offered- the first incorrect one, and then the second and correct one. Then consider the line you omit that is important to finish this out: 5....Rxa3.
The king controls the important square e3. If the king moves onto c4 instead of d4 it will lose a critical tempo.
And why does 4.Kd4 win and 4.Kc4 only draw?
Yancey, the problem slipped from my mind. Now you reminded me about it.
It's a winning position for white.