  Analyzing all 120 s and 20 s light curves obtained by the TESS satellite up
to Sector 69 - the end of the fifth year of observations - for all known white
dwarfs and white dwarf candidates up to G=17.5 mag, we report the discovery of
32 new pulsating DA white dwarf stars. For all objects, we obtained the period
spectra and performed a seismological analysis using full evolutionary models
to estimate the structural parameters, such as effective temperature, stellar
mass, and hydrogen envelope mass. The median stellar mass for the pulsators
from asteroseismology is 0.609 Msun, in agreement with the median value from
photometric and spectroscopic determinations, 0.602 Msun, excluding the low and
extremely-low mass objects. Finally, we found rotational-splitting multiplets
for 9 stars, which led to rotation periods between 4 h and 1 d.
