I'm absolutely clueless with this question

The answer is A, you may try to sub the coordinate to the equations when you don't know thr answer.
P(-5,0)
as its a rhombus, the sides are 5units
add a line from point Q to the x-axes to form a right-angled triangle,
PQ=5
5²=4²+x²
x=3
-5+3=-2 so Q(-2,4)
only option A can satisfy the coordinate