  In this work, we investigate the re-scattering effects in the radiative decay
$\Upsilon(5S)\to\eta_b+\gamma$, which were suggested to be crucially important
for understanding the anomalous largeness of the branching ratios
$B(\Upsilon(5S)\to \Upsilon(1S)+\pi\pi)$ and $B(\Upsilon(5S)\to
\Upsilon(1S)+\eta)$. Our calculations show that the re-scattering effects may
enhance $\Gamma(\Upsilon(10860)\to \eta_b+\gamma)$ by four orders, but the
tetraquark structure does not. Recently the BaBar and CLEO collaborations have
measured the mass of ${\eta_b}$ and the branching ratios
$\mathcal{B}(\Upsilon(2S)\rightarrow\eta_b+\gamma)$,
$\mathcal{B}(\Upsilon(3S)\rightarrow\eta_b+\gamma)$. We hope that very soon,
$\Upsilon(10860)\to \eta_b+\gamma$ will be measured and it would be an ideal
opportunity for testing whether the re-scattering or the tetraquark structure
is responsible for the anomaly of
$\mathcal{B}\big(\Upsilon(5S)\rightarrow\Upsilon(nS)\pi^+\pi^- (n=1,2,3)\big)$,
$i.e.$, the future measurements on the radiative decays of $\Upsilon(5S)$ might
be a touchstone of the two mechanisms.
