  We present a high-quality hard X-ray spectrum of the ultraluminous X-ray
source (ULX) NGC 5643 X-1 measured with NuSTAR in May-June 2014. We have
obtained this spectrum by carefully separating the signals from the ULX and
from the active nucleus of its host galaxy NGC 5643 located 0.8 arcmin away.
Together with long XMM-Newton observations performed in July 2009 and August
2014, the NuSTAR data confidently reveal a high-energy cutoff in the spectrum
of NGC 5643 X-1 above ~10 keV, which is a characteristic signature of ULXs. The
NuSTAR and XMM-Newton data are consistent with the source having a constant
luminosity ~1.5E40 erg/s (0.2-12 keV) in all but the latest observation (August
2014) when it brightened to ~3E40 erg/s. This increase is associated with the
dominant, hard spectral component (presumably collimated emission from the
inner regions of a supercritical accretion disc), while an additional, soft
component (with a temperature ~0.3 keV if described by multicolor disk
emission), possibly associated with a massive wind outflowing from the disk, is
also evident in the spectrum but does not exhibit significant variability.
