  We continue the constructive program about tensor field theory through the
next natural model, namely the rank five tensor theory with quartic melonic
interactions and propagator inverse of the Laplacian on $U(1)^5$. We make a
first step towards its construction by establishing its power counting,
identifiying the divergent graphs and performing a careful study of (a slight
modification of) its RG flow. Thus we give strong evidence that this just
renormalizable tensor field theory is non perturbatively asymptotically free.
