  Production of prompt D$^0$ mesons is studied in proton-lead and lead-proton
collisions recorded at the LHCb detector at the LHC. The data sample
corresponds to an integrated luminosity of $1.58\pm0.02$ nb$^{-1}$ recorded at
a nucleon-nucleon centre-of-mass energy of $\sqrt{s}=5$ TeV. Measurements of
the differential cross-section, the forward-backward production ratio and the
nuclear modification factor are reported using D$^0$ candidates with transverse
momenta less than 10 GeV/c and rapidities in the ranges $1.5<y^*<4.0$ and
$-5.0<y^*<-2.5$ in the nucleon-nucleon centre-of-mass system.
