The photoproduction of $J/\ensuremath{\psi}\phantom{\rule{1.111pt}{0ex}}$ mesons at low transverse momentum is studied in peripheral lead-lead collisions collected by the LHCb Collaboration at a center-of-mass energy per nucleon pair of $5\phantom{\rule{3.33333pt}{0ex}}\mathrm{TeV}$, corresponding to an integrated luminosity of 210 $\ensuremath{\mu}{\mathrm{b}}^{\ensuremath{-}1}$. The $J/\ensuremath{\psi}\phantom{\rule{1.111pt}{0ex}}$ 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.