To me a piece of cheese is what you might put in a mousetrap or maybe what a mouse might leave behind after helping itself to a whole slice of cheese. In the US we seldom speak of a serving of bread or cheese as a piece -- it's a slice, (or maybe a hunk or a chunk if torn off and not neatly sliced). A cheese sandwich is a slice of cheese between two slices of bread. But, oddly enough, we do speak of a piece of cake even though cakes are also served in slices.
You allowed "пять кусков хлеба" to be translated as "five slices of bread". While acknowledging differences in the construction of our sentences: as far as I am aware, there is no meaningful difference in the way Russian speakers and we Anglophones construct our sandwiches. It is nonsense to disallow the translation of "четыре куска сыра" as "four slices of cheese". Please, amend this lamentable state of affairs to introduce some clarity and consistency.