TH-TMO 2023 Problem 6

Let $a,b,c,x,y$ be positive real numbers such that $abc=1$ . Prove that $$\frac{a^5}{xc+yb}+\frac{b^5}{xa+yc}+\frac{c^5}{xb+ya}\geq \frac{9}{(x+y)(a^2+b^2+c^2)}.$$