What I heard in Moscow is that Khrushchev was impressed by the new-style architecture in Cuba, and imported the style to Moscow. It sounded like the reverse of what you say.
Of course not. Khrushchev started mass construction of series buildings. That means that all buildings in Chertanovo(Moscow) look like any other building in Voronezh. They're really uncomfortable. https://en.wikipedia.org/wiki/Khrushchyovka
Wait, shit, did I grow up in one? Serious question - I always imagined them as mostly built out of large concrete blocks, but all the examples there look like slightly shorter versions of my family's apartment in Moscow: http://i.imgur.com/dL34whm.jpg
It's not five stories, though.
That's "Plattenbau", a much later invention. Khruschevkas were built using traditional technology onsite, plattenbau is prefabricated and assembled in a fraction of time.