Step 1 :Factor the quadratic expression on the left side of the inequality, which gives \((x - 4)(x + 9)\).
Step 2 :Build a sign chart to determine the signs of the factors and the product in different intervals.
Step 3 :From the sign chart, we can see that \(x^2 + 5x - 36\) is less than or equal to 0 when \(-9 < x < 4\).
Step 4 :Also, \(f(x) = 0\) at \(x = 4\) and \(x = -9\).
Step 5 :Thus, the solution is \(x \in \boxed{[-9,4]}\).