The correct answer is $\boxed{\text{C}}$.
The intensity of a wave is proportional to the square of its amplitude. Therefore, the ratio of the intensities of two waves is equal to the square of the ratio of their amplitudes. In this case, the intensity ratio is 25:9, so the ratio of the amplitudes is $\sqrt{25:9} = \boxed{5:3}$.
Option A is incorrect because it is the square of the ratio of the amplitudes, not the ratio of the amplitudes itself. Option B is incorrect because it is the ratio of the amplitudes, not the square of the ratio of the amplitudes. Option D is incorrect because it is the inverse of the ratio of the amplitudes.