Explanation:
such a diamond or special kite is a rhombus.
especially interesting to us is that the diagonals intersect each other at their midpoints.
that means
y = 5
Pythagoras gets us x.
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle). in our case 13.
a and b are the 2 legs. in our case x and y.
13² = 5² + x²
169 = 25 + x²
x² = 169 - 25 = 144
x = sqrt(144) = 12