5. As shown in Figure 3, rectangle $B_{1} B C C_{1}$ is formed by joining square $B_{1} B A A_{1}$ and $A_{1} A C C_{1}$. Now, fold the figure along $A_{1} A$ to form a right dihedral angle, as shown in Figure 4. Take a point $P$ on line segment $B_{1} C$, and let the distance from $P$ to $A B$ be $P E$, and the distance from $P$ to $A_{1} C_{1}$ be $P F$. The relationship between $P E$ and $P F$ is ( ).
(A) $P E>P F$
(B) $P E=P F$
(C) $P E<P F$
(D) Cannot be determined, depends on the position of point $P$
5. (B).

As shown in Figure 15, if the shape is completed into a cube, then $B_{1} C$ is a body diagonal. Rotating around the body diagonal by $120^{\circ}$, $A_{1}$ becomes $B$, and $C_{1}$ becomes $A$. Therefore, the distance from point $P$ to $A_{1} C_{1}$, $P F$, becomes the distance from $P$ to $A B$, $P E$. Hence, $P F = P E$.