Longest cycles in 5-connected graphs

Let [Formula: see text] is an independent set of [Formula: see text][Formula: see text]. According to a theorem of Dirac, which states that if [Formula: see text] is a [Formula: see text]-connected graph on [Formula: see text] vertices and minimum degree [Formula: see text], then the circumference [Formula: see text], Cai, Li and Sun proved that if [Formula: see text] is a [Formula: see text]-connected graph on [Formula: see text] vertices, then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a [Formula: see text]-connected graph on [Formula: see text] vertices, then [Formula: see text].