  We present NuSTAR high energy X-ray observations of the pulsar wind nebula
(PWN)/supernova remnant G21.5-0.9. We detect integrated emission from the
nebula up to ~40 keV, and resolve individual spatial features over a broad
X-ray band for the first time. The morphology seen by NuSTAR agrees well with
that seen by XMM-Newton and Chandra below 10 keV. At high energies NuSTAR
clearly detects non-thermal emission up to ~20 keV that extends along the
eastern and northern rim of the supernova shell. The broadband images clearly
demonstrate that X-ray emission from the North Spur and Eastern Limb results
predominantly from non-thermal processes. We detect a break in the spatially
integrated X-ray spectrum at ~9 keV that cannot be reproduced by current SED
models, implying either a more complex electron injection spectrum or an
additional process such as diffusion compared to what has been considered in
previous work. We use spatially resolved maps to derive an energy-dependent
cooling length scale, $L(E) \propto E^{m}$ with $m = -0.21 \pm 0.01$. We find
this to be inconsistent with the model for the morphological evolution with
energy described by Kennel & Coroniti (1984). This value, along with the
observed steepening in power-law index between radio and X-ray, can be
quantitatively explained as an energy-loss spectral break in the simple scaling
model of Reynolds (2009), assuming particle advection dominates over diffusion.
This interpretation requires a substantial departure from spherical
magnetohydrodynamic (MHD), magnetic-flux-conserving outflow, most plausibly in
the form of turbulent magnetic-field amplification.
