Answer
$$\langle9,-11\rangle$$
Work Step by Step
$\vec{RS}$ is the vector from point $R:(-2,5)$ to $S:(2,-8).$
The change in the x-direction is
$$2-(-2)=4.$$
The change in the y-direction is
$$-8-5=-13.$$
So the vector can be written in component form as
$$\vec{RS}=\langle4,-13\rangle.$$
$\vec{PQ}$ is the vector from point $P:(-2,2)$ to $Q:(3,4).$
The change in the x-direction is
$$3-(-2)=5.$$
The change in the y-direction is
$$4-2=2.$$
So the vector can be written in component form as
$$\vec{PQ}=\langle5,2\rangle.$$
To get the sum of two vectors, add components.
$$\vec{RS}+\vec{PQ}=\langle4,-13\rangle+\langle5,2\rangle=\langle9,-11\rangle$$