  We report on a comparison between the theoretically predicted and
experimentally measured spectra of the first-forbidden non-unique $\beta$-decay
transition $^{137}\textrm{Xe}(7/2^-)\to\,^{137}\textrm{Cs}(7/2^+)$. The
experimental data were acquired by the EXO-200 experiment during a deployment
of an AmBe neutron source. The ultra-low background environment of EXO-200,
together with dedicated source deployment and analysis procedures, allowed for
collection of a pure sample of the decays, with an estimated
signal-to-background ratio of more than 99-to-1 in the energy range from 1075
to 4175 keV. In addition to providing a rare and accurate measurement of the
first-forbidden non-unique $\beta$-decay shape, this work constitutes a novel
test of the calculated electron spectral shapes in the context of the reactor
antineutrino anomaly and spectral bump.
