  We aim at constraining the dust mass in high-redshift ($z\gtrsim 5$) galaxies
using the upper limits obtained by ALMA in combination with the rest-frame
UV--optical spectral energy distributions (SEDs). For SED fitting, because of
degeneracy between dust extinction and stellar age, we focus on two extremes:
continuous star formation (Model A) and instantaneous star formation (Model B).
We apply these models to Himiko (as a representative UV-bright object) and a
composite SED of $z>5$ Lyman break galaxies (LBGs). For Himiko, Model A
requires a significant dust extinction, which leads to a high dust temperature
$>70$ K for consistency with the ALMA upper limit. This high dust temperature
puts a strong upper limit on the total dust mass $M_\mathrm{d}\lesssim 2\times
10^6$ M$_{\odot}$, and the dust mass produced per supernova (SN)
$m_\mathrm{d,SN}\lesssim 0.1$ M$_{\odot}$. Such a low $m_\mathrm{d,SN}$
suggests significant loss of dust by reverse shock destruction or outflow, and
implies that SNe are not the dominant source of dust at high $z$. Model B
allows $M_\mathrm{d}\sim 2\times 10^7$ M$_{\odot}$ and $m_\mathrm{d,SN}\sim
0.3$ M$_{\odot}$.} We could distinguish between Models A and B if we observe
Himiko at {wavelength $<$ 1.2 mm by ALMA. For the LBG sample, we obtain
$M_\mathrm{d}\lesssim 2\times 10^6$ M$_{\odot}$ for a typical LBG at $z>5$, but
this only puts an upper limit for $m_\mathrm{d,SN}$ as $\sim 2$ M$_{\odot}$.
This clarifies the importance of observing UV-bright objects (like Himiko) to
constrain the dust production by SNe.
