$\DeclareMathOperator\cl{cl}$The **cyclic edge connectivity** $\cl(G)$ is the size of a smallest cyclic edge cut, i.e., a smallest edge cut $F$ such that $G-F$ has two connected components, each of which contains at least one cycle.

In the paper *On the cyclic connectivity of planar graphs, Lecture Notes in Math. 303 (1972) 235–242.* by M.D. Plummer, Plummer proved the elegant Theorem 4 and leaves an open Question.

**Theorem 4.** If $G$ is planar and 5-connected, then $\cl(G) \le 13$.

Plummer presented an example of a 5-connected planar graph G with $\cl(G) = 10$. But he claimed that it is unknown whether 5-connected planar graphs with $\cl = 11, 12,$ or $13$ exist.

After searching the literature, I haven't found any related results. Has this question been resolved?