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We report results of the first detailed spectral and temporal studies of therecently discovered Be/X-ray binary eRASSU J050810.4$-$660653 in LMC based onthe data from the SRG/ART-XC, NuSTAR and Swift/XRT instruments obtained inDecember 2021 - May 2022 in a wide energy range of 0.5-79 keV. Pulsations withthe period of $40.5781 \pm 0.0004$ s were found in the source light curve withthe pulsed fraction monotonically increasing with the energy. An estimate ofthe orbital period of $\sim38$ days was obtained based on the long-termmonitoring of the system. The source spectrum can be well approximated with apower-law model modified by an exponential cutoff at high energies. The pulsephase-resolved spectroscopy shows a strong variation of spectral parametersdepending on the phase of a neutron star rotation. We have not found anyfeatures connected with the cyclotron absorption line both in thephase-averaged and phase-resolved spectra of eRASSU J050810.4$-$660653.However, the neutron star magnetic field was estimated around several $10^{13}$G using different indirect methods. Discovered variations of the hardness ratioover the pulse phase is discussed in terms of physical and geometricalproperties of the emitting region.

First characterization of a new High Mass X-ray Binary in LMC eRASSU J050810.4$-$660653 with SRG/ART-XC, NuSTAR and Swift