Explore a comprehensive lecture on Khovanov homology and its application to the (2,5) torus knot, also known as the cinquefoil. Delve into the intricate proof presented by Steven Sivek from Imperial College London, in collaboration with John Baldwin and Ying Hu. Discover how Khovanov homology can detect this specific torus knot without relying on knot Floer homology. Examine the integration of advanced concepts in Floer homology and recent developments in Khovanov homology and homotopy. Gain insights into this complex mathematical topic through a 59-minute presentation at the Institut Henri Poincaré, suitable for those with a strong background in advanced topology and knot theory.