The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower…

Given that the elevation to the top of the tower from the feet of one person due south is $=45°$

Similarly the angle of elevation to the top of tower from the feet of another person to the west of tower is $=30°$

The given information can be represented in the form of a diagram as below:

We need to find the distance $AB$.

Let the distance of $A,B$ from the tower be $x_1,x_2$.
$\Rightarrow \tan {45}^{°}=\frac{5}{x_1}, \tan {30}^{°}=\frac{5}{x_2}$
$\Rightarrow x_1=5, x_2=5\sqrt{3}$.

$\Rightarrow AB=\sqrt{{x_1}^2+{x_2}^2}=\sqrt{{\left(5\right)}^2+{\left(5\sqrt{3}\right)}^2}=10 m$

Hence this is the correct option.