  One of the most puzzling questions in neutrino physics is the origin of the
excess at 5 MeV in the reactor antineutrino spectrum. In this paper, we explore
the excess via the reaction $^{13}$C$(\overline{\nu}, \overline{\nu}^\prime
n)^{12}$C$^*$ in organic scintillator detectors. The de-excitation of
$^{12}$C$^*$ yields a prompt $4.4$ MeV photon, while the thermalization of the
product neutron causes proton recoils, which in turn yield an additional prompt
energy contribution with finite width. Together, these effects can mimic an
inverse beta decay event with around 5 MeV energy. We consider several
non-standard neutrino interactions to produce such a process and find that the
parameter space preferred by Daya Bay is disfavored by measurements of
neutrino-induced deuteron disintegration and coherent elastic neutrino-nucleus
scattering. While non-minimal particle physics scenarios may be viable, a
nuclear physics solution to this anomaly appears more appealing.
