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

The correct option is 4√2 units.

To find the distance between the two points A (-5, 7) and B (-1, 3), we use the distance formula in a two-dimensional Cartesian coordinate system. The formula for the distance between two points is:

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

Let the coordinates of point A be represented by:
$(x_1,y_1)=(-5,7)$
And let the coordinates of point B be represented by:
$(x_2,y_2)=(-1,3)$

First, calculate the difference in the x-coordinates:
$x_2-x_1=-1-(-5)=-1+5=4$
Next, calculate the difference in the y-coordinates:
$y_2-y_1=3-7=-4$

Substitute these differences back into the distance formula:
$d=\sqrt{{\left(4\right)}^2+{(-4)}^2}$
Evaluate the squares:
$4^2=16$
${(-4)}^2=16$
Add the results inside the square root:
$d=\sqrt{16+16}=\sqrt{32}$

Simplify the radical to its simplest form:
$d=\sqrt{16\times 2}=4\sqrt{2}$
Therefore, the distance between points A and B is 4√2 units.