  Building upon the classification by Lacini [arXiv:2005.14544], we determine
the isomorphism classes of log del Pezzo surfaces of rank one over an
algebraically closed field of characteristic five either which are not log
liftable over the ring of Witt vectors or whose singularities are not feasible
in characteristic zero. We also show that the Kawamata-Viehweg vanishing
theorem for ample $\mathbb{Z}$-Weil divisors holds for log del Pezzo surfaces
of rank one in characteristic five if those singularities are feasible in
characteristic zero.
