The correct answer is $\boxed{\text{A}}$.
The angular velocity is the rate of change of angular displacement. It is measured in radians per second (rad/s). The linear velocity is the rate of change of linear displacement. It is measured in meters per second (m/s).
The relationship between linear velocity and angular velocity is given by the following equation:
$$v = \omega r$$
where $v$ is the linear velocity, $\omega$ is the angular velocity, and $r$ is the radius of the object.
In this case, the linear velocity is given as $50 \text{ m/s}$ and the radius is given as $5 \text{ m}$. Substituting these values into the equation, we get:
$$v = \omega r = 50 \text{ m/s} = \omega \times 5 \text{ m}$$
Solving for $\omega$, we get:
$$\omega = \frac{v}{r} = \frac{50 \text{ m/s}}{5 \text{ m}} = 10 \text{ rad/s}$$
Therefore, the angular velocity of the point on the rim of the wheel is $\boxed{10 \text{ rad/s}}$.
Option A is the correct answer because it is the only option that is equal to $10 \text{ rad/s}$. Option B is incorrect because it is equal to $15 \text{ rad/s}$. Option C is incorrect because it is equal to $10 \text{ rad/s}$. Option D is incorrect because it is equal to $5 \text{ rad/s}$.