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We extend the proof from arXiv:1012.3137, which interprets the AGT relationas the Hubbard-Stratonovich duality relation to the case of 5d gauge theories.This involves an additional q-deformation. Not surprisingly, the extensionturns out to be trivial: it is enough to substitute all relevant numbers byq-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sumsand the Jack polynomials by the MacDonald ones. The problem with extra poles inindividual Nekrasov functions continues to exist, therefore, such a proof worksonly for \beta = 1, i.e. for q=t in MacDonald's notation. For \beta\ne 1 theconformal blocks are related in this way to a non-Nekrasov decomposition of theLMNS partition function into a double sum over Young diagrams.

Proving AGT conjecture as HS duality: extension to five dimensions