Series Solutions · Challenge problem

Solve $x\,y'' + y = 0$ with $y(2) = 1$, $y'(2) = 0$ by a power series about the ordinary point $x_0 = 2$, $y = \sum_{n=0}^{\infty} b_n (x-2)^n$. Find $b_5$. Express your answer as a common fraction.