  In this work, we consider the energy-supercritical defocusing cubic nonlinear
wave equation in dimension d=5 for radially symmetric initial data. We prove
that an a priori bound in the critical space implies global well-posedness and
scattering. The main tool that we use is a frequency localized version of the
classical Morawetz inequality, inspired by recent developments in the study of
the mass and energy critical nonlinear Schr\"odinger equation.
