  We measure the lifetime of the cesium $5^2D_{5/2}$ state using a
time-resolved single-photon-counting method. We excite atoms in a hot vapor
cell via an electric quadrupole transition at a wavelength of
$685\,\mathrm{nm}$ and record the fluorescence of a cascade decay at a
wavelength of $852\,\mathrm{nm}$. We extract a lifetime of
$1353(5)\,\mathrm{ns}$ for the $5^2D_{5/2}$ state, in agreement with a recent
theoretical prediction. In particular, the observed lifetime is consistent with
the literature values of the polarizabilities of the cesium $6P$ states. Our
measurement contributes to resolving a long-standing disagreement between a
number of experimental and theoretical results.
