  The photo-production of $J/\psi$ mesons at low transverse momentum is studied
in peripheral lead-lead collisions collected by the LHCb experiment at a
centre-of-mass energy per nucleon pair of 5 TeV, corresponding to an integrated
luminosity of 210 $\rm{\mu b}^{-1}$. The $J/\psi$ candidates are reconstructed
through the prompt decay into two muons of opposite charge in the rapidity
region of $2.0<y<4.5$. The results significantly improve previous measurements
and are compared to the latest theoretical prediction.
