The correct answer is $\boxed{\text{B}}$.
The equation of motion of a particle starting from rest along a straight line is $x = t^3 – 3t^2 + 5$. The velocity of the particle is $v = \frac{dx}{dt} = 3t^2 – 6t$.
The velocity after 5 seconds is $v(5) = 3(5)^2 – 6(5) = 45 – 30 = 15$.
The velocity after 3 seconds is $v(3) = 3(3)^2 – 6(3) = 27 – 18 = 9$.
The ratio of the velocities after 5 seconds and 3 seconds is $\frac{v(5)}{v(3)} = \frac{15}{9} = \boxed{2}$.
Option A is incorrect because the velocity after 5 seconds is not 2 times the velocity after 3 seconds.
Option B is correct because the ratio of the velocities after 5 seconds and 3 seconds is 2.
Option C is incorrect because the velocity after 5 seconds is not 3 times the velocity after 3 seconds.
Option D is incorrect because the velocity after 5 seconds is not 5 times the velocity after 3 seconds.