  Context. Massive substellar companions orbiting active low-mass stars are
rare. They, however, offer an excellent opportunity to study the main
mechanisms involved in the formation and evolution of substellar objects. Aims.
We aim to unravel the physical nature of the transit signal observed by the
TESS space mission on the active M dwarf TOI-5375. Methods. We analysed the
available TESS photometric data as well as high-resolution (R $\sim$ 115000)
HARPS-N spectra. We combined these data to characterise the star TOI-5375 and
to disentangle signals related to stellar activity from the companion transit
signal in the light-curve data. We ran an MCMC analysis to derive the orbital
solution and apply state-of-the-art Gaussian process regression to deal with
the stellar activity signal. Results. We reveal the presence of a companion in
the brown dwarf / very-low-mass star boundary orbiting around the star
TOI-5375. The best-fit model corresponds to a companion with an orbital period
of 1.721564 $\pm$ 10$^{\rm -6}$ d, a mass of 77 $\pm$ 8 $M_{\rm J}$ and a
radius of 0.99 $\pm$ 0.16 $R_{\rm J}$. Conclusions. We derive a rotation period
for the host star of 1.9692 $\pm$ 0.0004 d, and we conclude that the star is
very close to synchronising its rotation with the orbital period of the
companion.
