5. Given a regular triangular prism $A B C-A_{1} B_{1} C_{1}$ with a height of 2 and a base edge length of 1, the center of the upper base $\triangle A_{1} B_{1} C_{1}$ is $P$. A plane $B C D \perp A P$ is made through the lower base edge $B C$, intersecting the edge $A A_{1}$ at $D$. Then the area of the section $B C D$ is $\qquad$
Let the midpoints of $B_{1} C_{1}$ and $B C$ be $E$ and $F$, respectively, and connect $A_{1} E, E F, A F, D F$. Then $A P \perp D F \Rightarrow \triangle A D F \sim \triangle A_{1} P A \Rightarrow \frac{D F}{P A}=\frac{A F}{A_{1} A}$, and $P A=\sqrt{4+\left(\frac{\sqrt{3}}{3}\right)^{2}}=\frac{\sqrt{39}}{3}$. Therefore, $D F=\frac{P A \cdot A F}{A_{1} A}=\frac{\frac{\sqrt{39}}{3} \cdot \frac{\sqrt{3}}{2}}{2}=\frac{\sqrt{13}}{4}$, so $S_{\triangle B C D}=\frac{1}{2} \cdot \frac{\sqrt{13}}{4}=\frac{\sqrt{13}}{8}$.