Planar Turán number of disjoint union of C₃ and C₅

The planar Turán number of H, denoted by ex₏ (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 ex₏ (n, H) is known if H=C_ Cₖ, where, k \3, 4\. In this paper, we determine the value ex₏ (n, C₃ C₅) =8n-133 and characterize the extremal graphs when n is sufficiently large.