In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4(-1)(H5(-1)) with constant mean curvature H satisfying H2 ＞ 64/63 (H2 ＞ 175/148 respectively) must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4(-1) (resp. H5(-1)) with constant mean curvature H satisfying H2 ＞ 64/63 (resp. H2 ＞175/148 ) must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].