Given a graph H, the Turán function ex(n,H) is the maximum number of edges in a graph on n vertices not containing H as a subgraph. For two graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let ϕ (n,H) be the smallest number ϕ such that any graph G of order n admits an H-decomposition with at most ϕ parts. Pikhurko and Sousa conjectured that ϕ (n,H) = ex(n,H) for χ (H) ≥ 3 and all sufficiently large n. Their conjecture has been verified by Özkahya and Person for all edge-critical graphs H. In this article, we consider the gem graphs gem4 and gem5. The graph gem4 consists of the path P 4 with four vertices a, b, c, d and edges ab, bc, cd plus a universal vertex u adjacent to a, b, c, d, and the graph gem5 is similarly defined with the path P 5 on five vertices. We determine the Turán functions ex(n, gem4) and ex(n, gem5), and verify the conjecture of Pikhurko and Sousa when H is the graph gem4 and gem5.