  This Letter reports the first measurement of the $^{235}$U
$\overline{\nu_{e}}$ energy spectrum by PROSPECT, the Precision Reactor
Oscillation and Spectrum experiment, operating 7.9m from the
85MW$_{\mathrm{th}}$ highly-enriched uranium (HEU) High Flux Isotope Reactor.
With a surface-based, segmented detector, PROSPECT has observed 31678$\pm$304
(stat.) $\overline{\nu_{e}}$-induced inverse beta decays (IBD), the largest
sample from HEU fission to date, 99% of which are attributed to $^{235}$U.
Despite broad agreement, comparison of the Huber $^{235}$U model to the
measured spectrum produces a $\chi^2/ndf = 51.4/31$, driven primarily by
deviations in two localized energy regions. The measured $^{235}$U spectrum
shape is consistent with a deviation relative to prediction equal in size to
that observed at low-enriched uranium power reactors in the
$\overline{\nu_{e}}$ energy region of 5-7MeV.
