To find the height of the building, you can use trigonometric functions. Here, the ladder forms a right-angled triangle with the wall and the ground, with the ladder being the hypotenuse.

Given:
- Length of the ladder (hypotenuse) $=10$ m
- Angle with the horizontal $={60}^{\circ }$

You need to find the height of the building, which is the length of the side opposite the angle of ${60}^{\circ }$. Use the sine function:

$$\sin (\theta )=\frac{\text{Opposite}}{\text{Hypotenuse}}$$

Here:
$$\sin ({60}^{\circ })=\frac{\text{Height}}{10}$$

The value of $\sin ({60}^{\circ })$ is $\frac{\sqrt{3}}{2}$. So:

$$\frac{\sqrt{3}}{2}=\frac{\text{Height}}{10}$$

Solving for the height:

$$\text{Height}=10\times \frac{\sqrt{3}}{2}=5\sqrt{3}$$

Thus, the height of the building is:

C. $5\sqrt{3}$ m