  In this work, we study the hadronic loop contribution to the $\Upsilon(5S)\to
\Upsilon(1^3D_J)\eta$ ($J=1,2,3$) transitions. We predict that the branching
ratios of $\Upsilon(5S)\to \Upsilon(1^3D_1)\eta$, $\Upsilon(5S)\to
\Upsilon(1^3D_2)\eta$ and $\Upsilon(5S)\to \Upsilon(1^3D_3)\eta$ can reach up
to $(0.5\sim5.1)\times10^{-3}$, $(0.7\sim7.5)\times10^{-3}$ and
$(0.9\sim9.6)\times10^{-4}$, respectively. Since these predicted hadronic
transitions of $\Upsilon(5S)$ are comparable with these observed
$\Upsilon(5S)\to \Upsilon(nS)\pi^+\pi^-$ $(n=1,2,3)$, we suggest future
experiment like Belle and BelleII to carry out the search for these anomalous
$\Upsilon(5S)\to \Upsilon(1^3D_J)\eta$ transitions.

High Energy Physics - Phenomenology;High Energy Physics - Experiment