The distance between points A (-5, 7) and B (-1, 3) is:

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

---

Point A: $(x_1, y_1) = (-5, 7)$

Point B: $(x_2, y_2) = (-1, 3)$

---

$d = \sqrt{(-1 - (-5))^2 + (3 - 7)^2}$

$d = \sqrt{(4)^2 + (-4)^2}$

$d = \sqrt{16 + 16}$

$d = \sqrt{32}$

---

$32 = 16 \times 2$

$\sqrt{32} = \sqrt{16 \times 2}$

$\sqrt{32} = \sqrt{16} \times \sqrt{2}$

$\sqrt{32} = 4\sqrt{2}$

---

Therefore, the distance between points A and B is $4\sqrt{2}$ units.