The list chromatic number ${\chi }_L(G)$ is defined to be the minimal $k$ such that for any assignment of a list of $k$ colours to each vertex of $G$ (perhaps different lists for different vertices) a colouring of each vertex by a colour on its list can be chosen such that adjacent vertices receive distinct colours.Does every planar graph $G$ have ${\chi }_L(G)\le 5$? Is this best possible?