The stratospheric Brewer-Dobson circulation (BDC) is an important element of climate as it determines the transport and distributions of key radiatively active atmospheric trace gases, which affect the Earth's radiation budget and surface climate. Here, we evaluate the interannual variability, climatology, and trends of the BDC in the ERA5 reanalysis and intercompare them with its predecessor, the ERA-Interim reanalysis, for the 1979-2018 period. We also assess the modulation of the circulation by the Quasi-Biennial Oscillation (QBO) and the El Niño-Southern Oscillation (ENSO), as well as the forcings of the circulation by the planetary and gravity wave drag. The comparison of ERA5 and ERA-Interim reanalyses shows a very good agreement in the morphology of the BDC and in its structural modulations by the natural variability related to QBO and ENSO. Despite the good agreement in the spatial structure, there are substantial and significant differences in the strength of the BDC and natural variability impacts on the BDC between the two reanalyses, particularly in the upper troposphere and lower stratosphere (UTLS) and in the upper stratosphere. Throughout most regions of the stratosphere, the variability and trends of the advective BDC are stronger in the ERA5 reanalysis due to stronger planetary and gravity wave forcings, except in the UTLS below 20 km where the tropical upwelling is up to 40 % weaker mainly due to a significantly weaker gravity wave forcing at the equatorial-ward upper flank of the subtropical jet. In the extratropics, the large-scale downwelling is stronger in ERA5 than in ERA-Interim that is linked to significant differences in planetary and gravity wave forcings in the upper stratosphere. Analysis of the BDC trend shows a global insignificant acceleration of the annual mean residual circulation with an acceleration rate of about 1.5 % decade.sup.-1 at 70 hPa due to the long-term intensification in gravity and planetary wave breaking, consistent with observed and modelled BDC changes. Our findings suggest that the advective BDC from the kinematic ERA5 reanalysis is well suited for climate model validation in the UTLS and mid-stratosphere when using the standard formula of zonally averaged zonal momentum equation. The reported differences between the two reanalyses may also affect the nudged climate model simulations. Therefore, additional studies are needed to investigate whether or not nudging climate models toward ERA5 reanalysis will reproduce the upwelling trends from free-running simulations and from ERA5. Finally, further studies are also needed to better understand the impact of the new non-orographic gravity wave parameterization scheme, higher model top, and the representation of the sponge layer in ERA5 on the differences in the upper stratosphere and polar regions.