We answer Ivan Gutman′s open problem of systematically evaluating the Wiener indices of pentagonal chains by a compact formula. This enables speedy evaluations by hand as well as easy automated checking. The general algorithm is also suitable for treating chains involving polygons with odd number of sides other than five in general. We also obtain independent and, consequent results of all-around relevance, both analogous to and widely divergent from that for hexagonal chains.
