5. Among the twelve face diagonals and four body diagonals of a cube, two diagonals are randomly selected. Then the probability that the two diagonals are skew lines is ( ).
(A) $\frac{7}{30}$
(B) $\frac{9}{20}$
(C) $\frac{7}{15}$
(D) None of the above results is correct
5. B.

Among the twelve face diagonals and four body diagonals of a cube, the number of ways to select two diagonals is
$$
\mathrm{C}_{16}^{2}=\frac{16 \times 15}{2}=120 \text {. }
$$

When the lines containing the two diagonals are skew lines, at least one of the two diagonals is a face diagonal.

Taking any one face diagonal, among the remaining eleven face diagonals, five face diagonals are skew to this diagonal. Since the count is in pairs, there are $\frac{12 \times 5}{2}=30$ pairs of skew lines in this case.

Taking any one face diagonal, among the four body diagonals, two body diagonals are skew to this diagonal. Thus, there are $12 \times 2=24$ pairs of skew lines in this case.

Therefore, the probability that the lines containing the two randomly selected diagonals are skew lines is $\frac{30+24}{120}=\frac{9}{20}$.