The paper is devoted to one open extremal problem in geometric function theory of complex variables associated with estimates of functional defined on the systems of non-overlapping domains. We consider problem of the maximum of product of inner radii of n nonoverlapping domains containing points of the unit circle and the power <$Egamma> of the inner radius of domain containing the origin. The problem was formulated in 1994 in the Dubinin paper in the journal "Russian Mathematical Surveys" in the list of unsolved problems and then repeated in his monograph in 2014. Currently it is not solved in general. In this paper we obtained a solution of the problem for five simply connected domains and power <$Egamma~symbol <174>~(1;~2,~57]> and generalized this result to the case of multidimensional complex space.

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