The formula for the relativistic length contraction is:
$\begin{align*}L = L_0 \sqrt{1 - v^2/c^2}\end{align*}$
Plug in $L_0 = 5 \mbox{ m}$ and $L = 3 \mbox{ m}$ and solve for $v$ to find that $v = 0.8 c$ . Hence answer (C) is correct.

Solution to 1986 Problem 69