  We compute the electromagnetic self-force acting on a charged particle held
in place at a fixed position r outside a five-dimensional black hole described
by the Schwarzschild-Tangherlini metric. Using a spherical-harmonic
decomposition of the electrostatic potential and a regularization prescription
based on the Hadamard Green's function, we express the self-force as a
convergent mode sum. The self-force is first evaluated numerically, and next
presented as an analytical expansion in powers of R/r, with R denoting the
event-horizon radius. The power series is then summed to yield a closed-form
expression. Unlike its four-dimensional version, the self-force features a
dependence on a regularization parameter s that can be interpreted as the
particle's radius. The self-force is repulsive at large distances, and its
behavior is related to a model according to which the force results from a
gravitational interaction between the black hole and the distribution of
electrostatic field energy attached to the particle. The model, however, is
shown to become inadequate as r becomes comparable to R, where the self-force
changes sign and becomes attractive. We also calculate the self-force acting on
a particle with a scalar charge, which we find to be everywhere attractive.
This is to be contrasted with its four-dimensional counterpart, which vanishes
at any r.
