An isosceles triangle has two sides which are the same length. With coordinates it's often easier and just as good to verify the same squared length; we skip the square root. But here the two sides we're interested in are parallel to the axes so the length calculation is easy.
P(0,-5), A(3,-5), L(3,-2)
|PA| = 3, the difference in the x coordinates, because the y coordinate are the same
|AL| = |-2 - -5| = 3, the difference in the y coordinates, because the x coordinates are the same
|PA| = |AL| so we have an isoscles triangle.
PA is parallel to the x axis and AL is parallel to the y axis PAL has a right angle at A.
So we have an isosceles right triangle, one of the two tired triangle of trig.
If that's not enough of a proof, we can verify we have a right triangle a few different ways. Let's just do it by the Pythagorean Theorem.
A is a right angle iff |PA|² + |AL|² = |PL|²
The left side is |PA|² + |AL|² = 3² + 3² = 18
|PL|² = (3 - 0)² + (-2 - -5)² = 18
They're the same so we have a right angle. √
