Functional Equation
Algebra
Suppose there exists a function $f:\mathbb{R}\to\mathbb{R}$ such that $5f(x) + x^2 f(-x) = 5$. Determine the value of $f(5)$.
The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.