  This paper is devoted to the study of renormalization of the quartic melonic
tensor model in dimension (=rank) five. We review the perturbative
renormalization and the computation of the one loop beta function, confirming
the asymptotic freedom of the model. We then define the Connes-Kreimer-like
Hopf algebra describing the combinatorics of the renormalization of this model
and we analyze in detail, at one- and two-loop levels, the Hochschild
cohomology allowing to write the combinatorial Dyson-Schwinger equations.
Feynman tensor graph Hopf subalgebras are also exhibited.
