  We study the propagation of massless scalar fields non-minimally coupled to
gravity in the background of five-dimensional Einstein-power-Maxwell black
holes, and using the WKB and the pseudospectral Chebyshev methods we obtain the
quasinormal frequencies (QNFs), which allow us to show the existence of stable
and unstable QNFs depending on the power $k$ of the nonlinear electrodynamics,
the $\xi$ parameter, which controls the strength of the non-minimal coupling,
and on the size of the black hole.
