5. \( h^{4}-256 \)

We start with the expression h⁴ − 256. Notice that it is a difference of two squares, since h⁴ can be written as (h²)² and 256 as 16². Thus, we have:   h⁴ − 256 = (h²)² − 16². Using the difference of squares formula, which is a² − b² = (a − b)(a + b), we set a = h² and b = 16. This gives:   h⁴ − 256 = (h² − 16)(h² + 16). Next, observe that h² − 16 is itself a difference of two squares, because 16 = 4². So, we factor further:   h² − 16 = (h − 4)(h + 4). Thus, the complete factorization is:   h⁴ − 256 = (h − 4)(h + 4)(h² + 16). Note that h² + 16 does not factor further over the real numbers (but it can be factored over the complex numbers if needed).