5. Given the rectangular prism $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, among the following twelve lines: $A B^{\prime}, B A^{\prime}, C D^{\prime}, D C^{\prime}$, $A D^{\prime}, D A^{\prime}, B C^{\prime}, C B^{\prime}, A C, B D, A^{\prime} C^{\prime}$, $B^{\prime} D^{\prime}$, how many pairs of skew lines are there?
(A) 30 pairs;
(B) 60 pairs;
(C) 24 pairs;
(D) 48 pairs.

Answer ( )
The given 12 lines are the diagonals on the faces of the rectangular prism \(A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}\). Taking the line \(A B^{\prime}\) as an example, the diagonals that intersect with it are \(A C, A D^{\prime}, B^{\prime} D^{\prime}, B^{\prime} C, A^{\prime} B\), and the diagonals that are parallel to it are \(D C^{\prime}\). Therefore, there are 5 diagonals that are skew to \(A B^{\prime}\): \(C D^{\prime}, A^{\prime} C^{\prime}, B D, B C^{\prime}, A^{\prime} D\). Generally, for each diagonal on the faces of the rectangular prism, there are five diagonals on the other five faces that are skew to it. Thus, the 12 diagonals form 60 pairs of skew diagonals (with repeated counts). However, in the above counting, each pair of skew lines is counted twice, so there are only 30 pairs of skew lines.