  DP-coloring (also known as correspondence coloring) is a generalization of
list coloring introduced recently by Dvo\v{r}\'ak and Postle (2017). In this
paper, we prove that every planar graph $G$ without $4$-cycles adjacent to
$k$-cycles is DP-$4$-colorable for $k=5$ and $6$. As a consequence, we obtain
two new classes of $4$-choosable planar graphs. We use identification of
verticec in the proof, and actually prove stronger statements that every
pre-coloring of some short cycles can be extended to the whole graph.
