Subdivisions of K5K5 in graphs containing K2,3K2,3

Seymour and, independently, Kelmans conjectured that every 5-connected nonplanar graph contains a subdivision of K5K5. We prove this conjecture for graphs containing K2,3K2,3. As a consequence, the Kelmans–Seymour conjecture is true if the answer to the following question of Mader is affirmative: Does every simple graph on n≥4n≥4 vertices with more than 12(n−2)/512(n−2)/5 edges contain a K4−, a K2,3K2,3, or a subdivision of K5K5?