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

To factor \( h^{4}-256 \), recognize that this is a difference of squares, which can be expressed as \( (h^{2})^{2} - (16)^{2} \). This allows us to factor it into \( (h^{2} - 16)(h^{2} + 16) \). Further, \( h^{2} - 16 \) can be factored again as \( (h - 4)(h + 4) \). So the complete factorization is \( (h - 4)(h + 4)(h^{2} + 16) \). Another interesting tidbit: the expression \( h^{2} + 16 \) does not factor over the real numbers because it has no real roots (its roots are complex: \( 4i \) and \( -4i \)). This emphasizes how some polynomials can have a rich structure, showcasing both real and complex numbers in their factorization!