  WKB approximation methods are applied to the case of a massive scalar field
around a 5-dimensional Reissner-Nordstr\"om black hole. The divergences are
explicitly isolated and the cancellation against the Schwinger-De Witt
counter-terms proven. The resulting finite quantity is evaluated for different
values of the free parameters, namely the black hole mass and charge, and the
scalar field mass. We thus extend our previous results on quantum vacuum
polarization effects for uncharged asymptotically flat higher dimensional black
holes to electrically charged black holes.
