  DP-coloring is a generalization of a list coloring in simple graphs. Many
results in list coloring can be generalized in those of DP-coloring. Kim and
Ozeki showed that planar graphs without $k$-cycles where $k=3,4,5,$ or $6$ are
DP-$4$-colorable. Recently, Kim and Yu extended the result on $3$- and
$4$-cycles by showing that planar graphs without triangles adjacent to
$4$-cycles are DP-$4$-colorable. Xu and Wu showed that planar graphs without
$5$-cycles adjacent simultaneously to $3$-cycles and $4$-cycles are
$4$-choosable. In this paper, we extend the result on $5$-cycles and triangles
adjacent to $4$-cycles by showing that planar graphs without $i$-cycles
adjacent simultaneously to $j$-cycles and $k$-cycles are DP-$4$-colorable when
$\{i,j,k\}=\{3,4,5\}.$ This also generalizes the result of Xu and Wu.
