  We calculate the graviton's $\beta$-function in $AdS$ string-theoretic
sigma-model, perturbed by vertex operators for Vasiliev's higher spin gauge
fields in $AdS_5$. The result is given by $\beta_{mn}=R_{mn}+4T_{mn}(g,u)$
(with the AdS radius set to 1 and the graviton polarized along the $AdS_5$
boundary), with the matter stress-energy tensor given by that of conformal
holographic fluid in $d=4$, evaluated at the temperature given by
$T={1\over{\pi}}$. The stress-energy tensor is given by
$T_{mn}={g_{mn}}+4u_mu_n+\sum_{N}T^{(N)}_{mn}$ where $u$ is the vector
excitation satisfying $u^2=-1$ and $N$ is the order of the gradient expansion
in the dissipative part of the tensor. We calculate the contributions up to
N=2. The higher spin excitations contribute to the $\beta$-function, ensuring
the overall Weyl covariance of the matter stress tensor. We conjecture that the
structure of gradient expansion in $d=4$ conformal hydrodynamics at higher
orders is controlled by the higher spin operator algebra in $AdS_5$.
