The work done by a constant force is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. It is given by the formula: $W = Fd \cos \theta$ Where: $W = \text{work done} = 25 \text{ J}$ $F = \text{force} = 5 \text{ N}$ $d = \text{displacement} = 10 \text{ m}$ $\theta = \text{angle between the force and the displacement vectors}$

Substituting the given values into the formula: $25 = 5 \times 10 \times \cos \theta$ $25 = 50 \cos \theta$ $\cos \theta = \frac{25}{50} = \frac{1}{2}$

Since $\cos 60^\circ = \frac{1}{2}$, the angle $\theta$ is $60^\circ$.