An action-reaction pair of forces involved in the launching of the rocket is:

Before the explosion, the combined rocket (sections A and B) has:
Total mass $M = m_A + m_B = 3 \text{ kg} + 2 \text{ kg} = 5 \text{ kg}$.
Initial velocity $u = 5 \text{ m} \cdot \text{s}^{-1}$ (upwards).

After the explosion:
Mass of section A: $m_A = 3 \text{ kg}$.
Mass of section B: $m_B = 2 \text{ kg}$.
Velocity of section B: $v_B = 8 \text{ m} \cdot \text{s}^{-1}$ (upwards).
Let the velocity of section A after the explosion be $v_A$.

The total momentum before the explosion equals the total momentum after the explosion. Let upwards be the positive direction.

$$M u = m_A v_A + m_B v_B$$ $$(5 \text{ kg})(5 \text{ m} \cdot \text{s}^{-1}) = (3 \text{ kg}) v_A + (2 \text{ kg})(8 \text{ m} \cdot \text{s}^{-1})$$ $$25 \text{ kg} \cdot \text{m} \cdot \text{s}^{-1} = 3 v_A + 16 \text{ kg} \cdot \text{m} \cdot \text{s}^{-1}$$

$$3 v_A = 25 - 16$$ $$3 v_A = 9$$ $$v_A = \frac{9}{3}$$ $$v_A = 3 \text{ m} \cdot \text{s}^{-1}$$

Since $v_A$ is positive, the direction is upwards.

$$\boxed{\text{3 m}\cdot\text{s}^{-1} \text{ upwards}}$$