The inequality $x^{4}-5 x^{2}+4 \geq 0$ can be solved by considering all the cases graphing using intervals all of the above

Step 1 ：Rewrite the inequality as \((x^{2}-4)(x^{2}-1) \geq 0\).

Step 2 ：Find the roots of the inequality, which are x = -2, -1, 1, 2.

Step 3 ：Divide the number line into intervals using these roots and test the sign of the inequality in each interval.

Step 4 ：The solution to the inequality is \(x \in [-1, 1] \cup [2, \infty) \cup (-\infty, -2]\).

Step 5 ：Final Answer: The solution to the inequality \(x^{4}-5 x^{2}+4 \geq 0\) is \(\boxed{x \in [-1, 1] \cup [2, \infty) \cup (-\infty, -2]}\).