Decomposition of cubic graphs with cyclic connectivity 5

Let G be a cyclically 5-connected cubic graph with a 5-edge-cut separating G into two cyclic components $G_1$ and $G_2$. We prove that each component $G_i$ can be completed to a cyclically 5-connected cubic graph by adding three vertices, unless $G_i$ is a cycle of length five. Our work extends similar results by Andersen et al. for cyclic connectivity 4 from 1988.