A strong k-edge-coloring of a graph G is a mapping \(\varphi \) : \(E(G)\longrightarrow \{1,\ldots , k\}\) , such that \(\varphi (e)\ne \varphi (e^{'})\) for every pair of distinct edges at distance at most two. In this paper, we prove \(\chi ^{'}_{s}(G)\le 3\varDelta +1\) for a planar graph with \(g(G)\ge 5\) and 5-cycles are disjoint with \(6^{-}\) -cycles by analyzing the structural properties of minimal counterexample and using the discharging method.