  The production cross-sections of $\Upsilon$ mesons, namely $\Upsilon(1S)$,
$\Upsilon(2S)$ and $\Upsilon(3S)$, in $pp$ collisions at $\sqrt{s}=5 \
\rm{TeV}$ are measured with a data sample corresponding to an integrated
luminosity of $9.13\pm{0.18} \ \rm{pb}^{-1}$ collected by the LHCb detector.
The $\Upsilon$ mesons are reconstructed in the decay mode $\Upsilon \to {\mu}^+
{\mu}^-$. Double differential cross-sections times branching fractions, as
functions of the transverse momentum $p_{\rm{T}}$ and the rapidity $y$ of the
$\Upsilon$ mesons, are measured in the range $p_{\rm{T}} < 20 \ \rm{GeV}/c$ and
$2.0<y<4.5$. The results integrated over these $p_{\rm{T}}$ and $y$ ranges are
  $\sigma(\Upsilon(1S)) \times\mathcal{B}(\Upsilon(1S)\to {\mu}^+ {\mu}^-) =
2101\pm33\pm83 \ \rm{pb},$
  $\sigma(\Upsilon(2S)) \times\mathcal{B}(\Upsilon(2S)\to {\mu}^+ {\mu}^-) =
526\pm20\pm21 \ \rm{pb},$
  $\sigma(\Upsilon(3S)) \times\mathcal{B}(\Upsilon(3S)\to {\mu}^+ {\mu}^-) =
242\pm16\pm10 \ \rm{pb},$
  where the first uncertainties are statistical and the second are systematic.
The ratios of cross-sections between measurements of two different $\Upsilon$
states and between measurements at different center-of-mass energies are
determined. The nuclear modification factor of $\Upsilon(1S)$ at $\sqrt{s}=5 \
\rm{TeV}$ is updated as well using the directly measured cross-section results
from this analysis.
