#### Answer

$Q(3,-4)$

#### Work Step by Step

To find the midpoint between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the midpoint formula:
$\displaystyle Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
We have the two points, $P(7,10)$ and $Q(x,y)$. The midpoint is $M(5,3)$. Thus we have:
$\displaystyle Midpoint=(\frac{7+x}{2},\ \frac{10+y}{2})=(5,3)$
We solve for $x$:
$\frac{7+x}{2}=5$
$7+x=10$
$x=3$
And for $y$:
$\frac{10+y}{2}=3$
$10+y=6$
$y=-4$
Therefore, the point Q is: $(3,-4)$