5. Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length $a$, and $E$ is the midpoint of edge $D D_{1}$. Then the area of the section passing through point $C$ and perpendicular to line $B E$ is $\qquad$ .
5. $\frac{9 a^{2}}{8}$.

Take the midpoints of edges $A_{1} B_{1}$ and $B_{1} C_{1}$ as $F$ and $G$, respectively. It is easy to see that quadrilateral $A C G F$ is the desired cross-section, and it is an isosceles trapezoid. The area can be calculated as $\frac{9 a^{2}}{8}$.