5. As shown in Figure 1, in the cube $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, there is a point $M$ on the side face $A A^{\prime} B^{\prime} B$ such that the distances from $M$ to the two lines $A B$ and $B^{\prime} C^{\prime}$ are equal. Then, the trajectory of $M$ is ( ).
(A) a part of a parabola
(B) a part of a hyperbola
(C) a part of an ellipse
(D) a line segment
5.A.

Since $B^{\prime} C^{\prime} \perp$ plane $A A^{\prime} B^{\prime} B$, it follows that $M B^{\prime} \perp B^{\prime} C^{\prime}$. Therefore, the distance from $M$ to point $B^{\prime}$ is equal to the distance from $M$ to line $A B$. Thus, the locus of $M$ is part of a parabola.