  This article reports the measurement of the $^{235}$U-induced antineutrino
spectrum shape by the STEREO experiment. 43'000 antineutrinos have been
detected at about 10 m from the highly enriched core of the ILL reactor during
118 full days equivalent at nominal power. The measured inverse beta decay
spectrum is unfolded to provide a pure $^{235}$U spectrum in antineutrino
energy. A careful study of the unfolding procedure, including a
cross-validation by an independent framework, has shown that no major biases
are introduced by the method. A significant local distortion is found with
respect to predictions around $E_\nu \simeq 5.3$ MeV. A gaussian fit of this
local excess leads to an amplitude of $A = 12.1 \pm 3.4\%$ (3.5$\sigma$).
