The theory of m-th root Finsler metrics has been applied to Ecology, Biology, Seismic Ray Theory, Gravitation, etc. It is regarded as a direct generalization of Riemannian metric in a sense, that is, the second root metric is a Riemannian metric. On the other hand, the Riemannian curvature faithfully reveals the local geometric properties of a Riemann-Finsler metric. In this paper, we study the class of quintic (𝛼.𝛽)-metrics. We show that 5-root (𝛼.𝛽)-metrics have an unbound Cartan torsion.
