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.
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