The acceleration due to gravity at a depth 10 km below the earth is the same as at a height h above the surface of earth. Then:

The acceleration due to gravity at a height  h  is given as:

$g_h=g\left(1-\frac{2h}{R_e}\right)$

$\text{ where }{R}_e\text{ is radius of earth. }$

The acceleration due to gravity at a depth  d  is given as:

$g_d=g\left(1-\frac{d}{R_e}\right)$

$\text{ Given, }{g}_h=g_d$

$\therefore g\left(1-\frac{2h}{R_e}\right)=g\left(1-\frac{d}{R_e}\right)$

$$\begin{gathered} \therefore \mathrm{d}=2\mathrm{h} \\ \Rightarrow \mathrm{h} =\frac{\mathrm{d}}{2} \\ \Rightarrow \mathrm{h} = \frac{10}{2} = 5 \mathrm{km} \end{gathered}$$