Answer
$$\color {blue}{\bf\text{No, the points don't make a right triangle}}$$
Work Step by Step
For clarity lets start by naming our points:
$A=(-2,-5)$
$B=(1,7)$
$C=(3,15)$
First, we'll use the distance formula to find the lengths of each side:
$d(P,Q)=\sqrt{(x_{P}-x_{Q})^2+(y_{P}-y_{Q})^2}$
$AB= \sqrt{(-2-1)^2+(-5-7)^2}$
$AB= \sqrt{(-3)^2+(-12)^2}$
$AB= \sqrt{9+144}$
$AB= \sqrt{153}$
$AC= \sqrt{(-2-3)^2+(-5-15)^2}$
$AC= \sqrt{(-5)^2+(-20)^2}$
$AC= \sqrt{25+400}$
$AC= \sqrt{425}$
$BC= \sqrt{(1-3)^2+(7-15)^2}$
$BC= \sqrt{(-2)^2+(-8)^2}$
$BC= \sqrt{4+64}$
$BC= \sqrt{68}$
Now that we have the lengths of the sides,
$AB=\sqrt{153}$, $AC= \sqrt{425}$, $BC=\sqrt{68}$,
we can apply the Pythagorean Theorem $a^2+b^2=c^2$ to see if the sides make a right triangle.
$(\sqrt{153})^2+(\sqrt{68})^2=(\sqrt{425})^2$
$153+68=425$
$221=425$
Which is $\bf \text{false}$, so:
$$\color {blue}{\bf\text{No, the points don't make a right triangle}}$$
