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The collection of high-quality photometric data by space telescopes isrevolutionizing the area of white-dwarf asteroseismology. Among the differentkinds of pulsating white dwarfs, there are those that have He-rich atmospheres,and they are called DBVs or V777 Her variable stars. The archetype of thesepulsating white dwarfs, GD~358, is the focus of the present paper. We report athorough asteroseismological analysis of the DBV star GD~358 (TIC~219074038)based on new high-precision photometric data gathered by the {\it TESS} spacemission combined with data taken from the Earth. In total, we detected 26periodicities from the {\it TESS} light curve of this DBV star using a standardpre-whitening. The oscillation frequencies are associated with nonradial$g$(gravity)-mode pulsations with periods from $\sim 422$ s to $\sim 1087$ s.Moreover, we detected 8 combination frequencies between $\sim 543$ s and $\sim295$ s. We combined these data with a huge amount of observations from theground. We found a constant period spacing of $39.25\pm0.17$ s, which helped usto infer its mass ($M_{\star}= 0.588\pm0.024 M_{\sun}$) and constrain theharmonic degree $\ell$ of the modes. We carried out a period-fit analysis onGD~358, and we were successful in finding an asteroseismological model with astellar mass ($M_{\star}= 0.584^{+0.025}_{-0.019} M_{\sun}$), in line with thespectroscopic mass ($M_{\star}= 0.560\pm0.028 M_{\sun}$). We found that thefrequency splittings vary according to the radial order of the modes,suggesting differential rotation. Obtaining a seismological made it possible toestimate the seismological distance ($d_{\rm seis}= 42.85\pm 0.73$ pc) ofGD~358, which is in very good accordance with the precise astrometric distancemeasured by {\it GAIA} EDR3 ($\pi= 23.244\pm 0.024, d_{\rm GAIA}= 43.02\pm0.04$~pc).

Pulsating hydrogen-deficient white dwarfs and pre-white dwarfs observed with {\it TESS}: III. Asteroseismology of the DBV star GD 358