  Building on previous results concerning hyperbolicity of groups of Fibonacci
type, we give an almost complete classification of the (non-elementary)
hyperbolic groups within this class. We are unable to determine the
hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups
H(9,4), H(9,7). We show that if H(9,4) is torsion-free then it is not
hyperbolic. We consider the class of T(5) cyclically presented groups and
classify the (non-elementary) hyperbolic groups and show that the Tits
alternative holds.
