For a given graph G=(V,E), let mathscrL(G)=L(v):vinV be a prescribed list assignment. G is mathscrL-L(2,1)-colorable if there exists a vertex labeling f of G such that f(v)inL(v) for all vinV; β£f(u)βf(v)β£geq2 if dGβ(u,v)=1; and β£f(u)βf(v)β£geq1 if dGβ(u,v)=2. If G is mathscrL-L(2,1)-colorable for every list assignment mathscrL with β£L(v)β£geqk for all vinV, then G is said to be k-L(2,1)-choosable. In this paper, we prove all cycles are 5-L(2,1)-choosable