Planar Turán number of disjoint union of C₃ and C₅

The planar Turán number of H, denoted by exP(n,H), is the maximum number of edges in an n-vertex H-free planar graph. The planar Turán number of k≥ 3 vertex-disjoint union of cycles is the trivial value $3n-6$. Let C_ denote the cycle of length and C_∪ Cₜ denote the union of disjoint cycles C_ and Cₜ. The planar Turán number exP(n,H) is known if H=C_∪ Cₖ, where ,k∈ \3,4\. In this paper, we determine the value exP(n,C₃∪ C₅)=8n-13/3 and characterize the extremal graphs when n is sufficiently large.