We report the discovery of five transiting companions near the hydrogen-burning mass limit in close orbits around main sequence stars originally identified by the Transiting Exoplanet Survey Satellite (TESS) as TESS Objects of Interest (TOIs): TOI-148, TOI-587, TOI-681, TOI-746, and TOI-1213. Using TESS and ground-based photometry as well as radial velocities from the CORALIE, CHIRON, TRES, and FEROS spectrographs, we found the companions have orbital periods between 4.8 and 27.2 days, masses between 77 and 98 $mathrm{M_{Jup}}$, and radii between 0.81 and 1.66 $mathrm{R_{Jup}}$. These targets have masses near the uncertain lower limit of hydrogen core fusion ($sim$73-96 $mathrm{M_{Jup}}$), which separates brown dwarfs and low-mass stars. We constrained young ages for TOI-587 (0.2 $pm$ 0.1 Gyr) and TOI-681 (0.17 $pm$ 0.03 Gyr) and found them to have relatively larger radii compared to other transiting companions of a similar mass. Conversely we estimated older ages for TOI-148 and TOI-746 and found them to have relatively smaller companion radii. With an effective temperature of 9800 $pm$ 200 K, TOI-587 is the hottest known main-sequence star to host a transiting brown dwarf or very low-mass star. We found evidence of spin-orbit synchronization for TOI-148 and TOI-746 as well as tidal circularization for TOI-148. These companions add to the population of brown dwarfs and very low-mass stars with well measured parameters ideal to test formation models of these rare objects, the origin of the brown dwarf desert, and the distinction between brown dwarfs and hydrogen-burning main sequence stars.
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