#### Answer

$(x+1)^2+(y-1)^2=16$

#### Work Step by Step

RECALL:
The standard form of the equation of a circle with a center at $(h, k)$ and a radius of $r$ units is:
$(x-h)^2+(y-k)^2=r^2$
The given circle has its center at $(-1, 1)$.
The point on the circle that is directly to the left of the center is $(-5, 1)$.
This point is 4 units away from the center.
This means that the radius is 4 units.
Since the center is at (-1, 1), we know that h=-1 and k = 1
The radius is 4 units, so r = 4.
Therefore, the equation of the given circle is:
$[(x-(-1)]^2 + (y-1)^2=4^2
\\(x+1)^2+(y-1)^2=16$