A　proper　edge　coloring　of　a　graph　G　is　acyclic　if　there　is　no　bichromatic　cycle　in　G.　The　acyclic　chromatic　index　of　G,　denoted　χa′(G),　is　the　least　number　of　colors　k　such　that　G　has　an　acyclic　k-edge-coloring.　In　this　paper,　it　is　shown　that　if　G　is　a　planar　graph　with　girth　at　least　5　and　maximum　degree　Δ,　then　χa′(G)≤Δ+1.　Moreover,　if　Δ≥9,　then　χa′(G)=Δ.　©　2013　Elsevier　B.V.　All　rights　reserved.