Answer
After the collision, the speed of the 5.0 kg object is $3.0~m/s$
Work Step by Step
Let $m_A = 1.0~kg$ and let $m_B = 5.0~kg$
Let $v_A$ be the initial velocity of the 1.0-kg object.
Let $v_B$ be the initial velocity of the 5.0-kg object.
Let $v_A'$ be the final velocity of the 1.0-kg object.
Let $v_B'$ be the final velocity of the 5.0-kg object.
We can use conservation of momentum to find the speed of the $5.0~kg$ object after the collision:
$m_A~v_A' + m_B~v_B' = m_A~v_A + m_B~v_B$
$m_B~v_B' = m_A~(v_A-v_A') + m_B~v_B$
$v_B' = \frac{m_A~(v_A-v_A') + m_B~v_B}{m_B}$
$v_B' = \frac{(1.0~kg)~[10.0~m/s-(-5.0~m/s)] + (5.0~kg)(0)}{5.0~kg}$
$v_B' = 3.0~m/s$
After the collision, the speed of the 5.0 kg object is $3.0~m/s$
