1. The problem is to solve the inequality $f(x) \geq 0$ given that the solution to $f(x) < 0$ is $(1, 5)$. 2. From the given solution for $f(x) < 0$, the function is negative between $x=1$ and $x=5$. 3. Because $f(x)$ is a parabola opening upwards and $f(x)<0$ on $(1,5)$, the function is zero or positive outside this interval. 4. Hence, the solution set to $f(x) \geq 0$ is the complement of $(1,5)$, which is $(-\infty, 1] \cup [5, \infty)$. 5. This means $f(x)$ is positive or zero for all $x \leq 1$ and for all $x \geq 5$. Final answer: $(-\infty, 1] \cup [5, \infty)$