5. In a regular triangular prism $A B C=A_{1} B_{1} C_{1}$, if $A B$ $=\sqrt{2} B B_{1}$, then the angle formed by $C A_{1}$ and $C_{1} B$ is ( ).
(A) $60^{\circ}$
(B) $75^{\circ}$
(C) $90^{\circ}$
(D) $105^{\circ}$
5. C.

Let the line containing $A_{1} B_{1}$ be the $x$-axis, the line perpendicular to $A_{1} B_{1}$ in the plane $A_{1} B_{1} C_{1}$ be the $y$-axis, and the line containing $B B_{1}$ be the $z$-axis to establish a spatial rectangular coordinate system. Then
$$
\begin{array}{l}
A_{1}(\sqrt{2}, 0,0), C_{1}\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{6}}{2}, 0\right), \\
C\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{6}}{2}, 1\right), B(0,0,1) . \\
\text { Therefore, } \overrightarrow{C A}=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{6}}{2},-1\right), \\
\overrightarrow{C_{1} B}=\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{6}}{2}, 1\right) .
\end{array}
$$

Thus, $\overrightarrow{C A_{1}} \cdot \overrightarrow{C_{1} B}=0$.