Answer
$$S(3,4)$$
Work Step by Step
We have the following points:
$P(0,3)$
$Q(2,2)$
$R(5,3)$
$S(x,y)$
According to the definition of a parallelogram, its diagonals intercept each other at the midpoint of each of them.
Using the midpoint formula $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$, we can calculate the midpoint $M$ using either the diagonal $PR$ or the diagonal $QS$.
$M_{PR}=(\frac{0+5}{2}, \frac{3+3}{2})=(2.5, 3)$
$M_{QS} = (\frac{2+x}{2}, \frac{2+y}{2})$
We also know, that these midpoints are on the same point $(M_{PR}=M_{QS})$. Which means:
$\frac{2+x}{2}=2.5$
$2+x=5$
$x=3$
$\frac{2+y}{2}=3$
$2+y=6$
$y=4$
We have found point $S(3,4)$