Given that the points are A$(-3,2)$, B$(-5,5)$, C$(2,-3)$ and D$(4,4)$
So, Coordinates of the mid-point of AC are $(-3+2/2,2-3/2)=(-1/2,-1/2)$
And,
The Coordinates of mid-point of BD are $(-5+4/2,-5+4/2)=(-1/2,-1/2)$
Therefore, the mid-point for both the diagonals are the same. Thus, ABCD is a parallelogram.
up next, the sides
It is clear that ABCD is a parallelogram with adjacent sides equal.
Hence, ABCD is a rhombus.
$AB=\sqrt{{{(-5+3)}^{2}}+{{(-5-2)}^{2}}}$
$AB=\sqrt{4+49}$
$AB=\sqrt{53}$
$BC=\sqrt{{{(-5-2)}^{2}}+{{(-5+3)}^{2}}}$
$BC=\sqrt{49+4}$
$BC=\sqrt{55}$
AB=BC