Disjoint triangles and pentagons in a graph

Let n, s, and t be integers with s ≥ 1, t ≥ 0, and n = 3s + 5t. Let G be a graph of order n such that the minimum degree of G is at least (n + s + t)/2. Then G contains s + t independent subgraphs such that s of them are triangles and t of them are pentagons.