DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák 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.Recently, Dvorák and Postle [2] introduced DP -coloring (also known as correspondence coloring) as a generalization of list coloring.Definition 1.1. Let G be a simple graph with n vertices and let L be a list assignment for V (G). For each edge uv in G, let M uv be a matching between the sets L(u) and L(v) and let M L = {M uv : uv ∈ E(G)}, called the matching assignment. Let H L be the graph that satisfies the following conditions

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