Neighbor sum distinguishing total colorings of planar graphs with girth at least 5

Let G = (V, E) be a graph and phi be a proper k-total coloring wof G. For a vertex v of G, let f(v) = Sigma(uv)is an element of E(G)phi(uv) + phi(v). The coloring phi is neighbor sum distinguishing if f(u) not equal f(v) for each edge uv E E(G). The smallest integer k in such a coloring of G is the neighbor sum distinguishing total chromatic number, denoted by x"(Sigma)(G). By using the famous Combinatorial Nullstellensatz, we determine chi"(Sigma)(G) for any planar graph G with girth at least 5 and Delta(G) >= 7.