**Step 1 — Use the key property.**
In a rhombus the **diagonals bisect each other**, so
$$\text{Mid-point of } PR = \text{Mid-point of } QS$$

**Step 2 — Find the mid-point of diagonal PR.**
$$M = \left(\frac{2 + (-2)}{2},\ \frac{-3 + 1}{2}\right) = \left(\frac{0}{2},\ \frac{-2}{2}\right) = (0,\ -1)$$

This point $M$ is also the point where the diagonals intersect.

**Step 3 — Let $S = (x, y)$ and use the mid-point of QS.**
$$\left(\frac{6 + x}{2},\ \frac{5 + y}{2}\right) = (0,\ -1)$$

**Step 4 — Equate and solve for $x$.**
$$\frac{6+x}{2} = 0 \ \Rightarrow\ 6 + x = 0 \ \Rightarrow\ x = -6$$

**Step 5 — Equate and solve for $y$.**
$$\frac{5+y}{2} = -1 \ \Rightarrow\ 5 + y = -2 \ \Rightarrow\ y = -7$$

**Step 6 — Final answer.**
$$\boxed{S(-6,\ -7) \quad \text{and} \quad \text{diagonals intersect at } (0,\ -1)}$$