  High-pressure single-crystal x-ray diffraction experiments reveal that the
superconducting kagome metal CsV$_3$Sb$_5$ transforms from hexagonal ($P6/mmm$)
to monoclinic ($C2/m$) symmetry above 10 GPa if nonhydrostatic pressure
conditions are created in a diamond anvil cell with silicon oil as
pressure-transmitting medium. This is contrary to the behavior of CsV$_3$Sb$_5$
under quasi-hydrostatic conditions in neon, with the hexagonal symmetry
retained up to at least 20 GPa. Monoclinic distortion leaves the kagome planes
almost unchanged but deforms honeycomb nets of the Sb atoms. While the onset of
the distortion almost coincides with the reentrance of superconductivity, our
\textit{ab initio} density-functional calculations reveal only minor changes in
the electronic structure compared to the quasi-hydrostatic case. In particular,
Fermi surface reconstruction driven by the formation of interlayer Sb-Sb bonds
is observed in both monoclinic and hexagonal CsV$_3$Sb$_5$ structures at high
pressures and comes out as the likely cause for the reentrant behavior.
