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