  We report $^{121/123}$Sb nuclear quadrupole resonance (NQR) and $^{51}$V
nuclear magnetic resonance (NMR) measurements on kagome metal CsV$_3$Sb$_5$
with $T_{\rm c}=2.5$ K. Both $^{51}$V NMR spectra and $^{121/123}$Sb NQR
spectra split after a charge density wave (CDW) transition, which demonstrates
a commensurate CDW state. The coexistence of the high temperature phase and the
CDW phase between $91$ K and $94$ K manifests that it is a first order phase
transition. At low temperature, electric-field-gradient fluctuations diminish
and magnetic fluctuations become dominant. Superconductivity emerges in the
charge order state. Knight shift decreases and $1/T_{1}T$ shows a
Hebel--Slichter coherence peak just below $T_{\rm c}$, indicating that
CsV$_3$Sb$_5$ is an s-wave superconductor.

Superconductivity;Strongly Correlated Electrons