  The {\sl TESS} space mission has recently demonstrated its great potential to
discover new pulsating white dwarf and pre-white dwarf stars, and to detect
periodicities with high precision in already known white-dwarf pulsators. We
report the discovery of two new pulsating He-rich atmosphere white dwarfs
(DBVs) and present a detailed asteroseismological analysis of three already
known DBV stars employing observations collected by the {\sl TESS} mission
along with ground-based data. We extracted frequencies from the {\sl TESS}
light curves of these DBV stars using a standard pre-whitening procedure to
derive the potential pulsation frequencies. All the oscillation frequencies
that we found are associated with $g$-mode pulsations with periods spanning
from $\sim 190$ s to $\sim 936$ s. We find hints of rotation from frequency
triplets in some of the targets, including the two new DBVs. For three targets,
we find constant period spacings, which allowed us to infer their stellar
masses and constrain the harmonic degree $\ell$ of the modes. We also performed
period-to-period fit analyses and found an asteroseismological model for three
targets, with stellar masses generally compatible with the spectroscopic
masses. Obtaining seismological models allowed us to estimate the seismological
distances and compare them with the precise astrometric distances measured with
{\it Gaia}. We find a good agreement between the seismic and the astrometric
distances for three stars (PG~1351+489, EC~20058$-$5234, and EC~04207$-$4748),
although for the other two stars (WD~J152738.4$-$50207 and WD~1708$-$871), the
discrepancies are substantial. The high-quality data from the {\sl TESS}
mission continue to provide important clues to determine the internal structure
of pulsating pre-white dwarf and white dwarf stars through the tools of
asteroseismology.
