  We consider the U(n)xU(m) symmetric Phi^4 Lagrangian to describe the
finite-temperature phase transition in QCD in the limit of vanishing quark
masses with n=m=N_f flavors and unbroken anomaly at T_c. We compute the
Renormalization Group functions to five-loop order in Minimal Subtraction
scheme. Such higher order functions allow to describe accurately the
three-dimensional fixed-point structure in the plane (n,m), and to reconstruct
the line n^+(m,d) which limits the region of second-order phase transitions by
an expansion in epsilon=4-d. We always find n^+(m,3)>m, thus no
three-dimensional stable fixed point exists for $n=m$ and the finite
temperature transition in light QCD should be first-order. This result is
confirmed by the pseudo-epsilon analysis of massive six-loop three dimensional
series.

High Energy Physics - Phenomenology;Statistical Mechanics;High Energy Physics - Lattice