5. Let the complex number $z$ be such that the real and imaginary parts of $\frac{z}{10}$ and $\frac{10}{\bar{z}}$ are both positive numbers less than 1. The set of points corresponding to $z$ in the complex plane forms a figure $c$. Then the area of $c$ is ().
A. 100
B. $75-\frac{25}{2} \pi$
C. $75+\frac{25}{4} \pi$
D. $100 \pi$
5. B

Let $z=x+y i$, then $\frac{z}{10}=\frac{x}{10}+\frac{y}{10} i \quad \frac{10}{z}=\frac{10 x}{x^{2}+y^{2}}+\frac{10 y}{x^{2}+y^{2}} i$
From the given conditions, it is easy to know $05^{2}$
$x^{2}+(y-5)^{2}>5^{2}$
Thus, the figure $c$ is the shaded part as shown, and it is not difficult to find that its area is $10^{2}-2 \cdot \frac{5 \pi^{2}}{4}-5^{2}=$ $75-\frac{25}{2} \pi$