Answer: To determine the gradient of the line between the point (0, -3) on the circle and the center of the circle, we need to find the center of the circle first.
The equation of the circle is given as (x + 5)^2 + (y + 2)^2 = 26. This is in the standard form of the circle equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.
Comparing the given equation with the standard form, we can see that h = -5 and k = -2. So, the center of the circle is (-5, -2).
Now, we can find the gradient (slope) of the line between the point (0, -3) and the center (-5, -2) using the formula for slope:
Gradient (m) = (change in y) / (change in x)
Change in y = -2 - (-3) = 1
Change in x = -5 - 0 = -5
Gradient (m) = 1 / -5
Therefore, the gradient of the line between the point (0, -3) on the circle and the center of the circle (-5, -2) is -1/5.