We report results of the first detailed spectral and temporal studies of the recently discovered Be/X-ray binary eRASSU J050810.4-660653 in Large Magellanic Cloud based on the data from the SRG/ART-XC, NuSTAR and Swift/XRT instruments obtained in 2021 December-2022 May in a wide energy range of 0.5-79 keV. Pulsations with the period of 40.5781 ± 0.0004 s were found in the source light curve with the pulsed fraction monotonically increasing with the energy. An estimate of the orbital period of ?38 d was obtained based on the long-Term monitoring of the system. The source spectrum can be well approximated with a power-law model modified by an exponential cutoff at high energies. The pulse phase-resolved spectroscopy shows a strong variation of spectral parameters depending on the phase of a neutron star rotation. We have not found any features connected with the cyclotron absorption line both in the phase-Averaged and phase-resolved spectra of eRASSU J050810.4-660653. However, the neutron star magnetic field was estimated around several 1013 G using different indirect methods. Discovered variations of the hardness ratio over the pulse phase is discussed in terms of physical and geometrical properties of the emitting region.