  We answer positively the question of Albertson asking whether every planar
graph can be $5$-list-colored even if it contains precolored vertices, as long
as they are sufficiently far apart from each other. In order to prove this
claim, we also give bounds on the sizes of graphs critical with respect to
5-list coloring. In particular, if G is a planar graph, H is a connected
subgraph of G and L is an assignment of lists of colors to the vertices of G
such that |L(v)| >= 5 for every v in V(G)-V(H) and G is not L-colorable, then G
contains a subgraph with O(|H|^2) vertices that is not L-colorable.
