The equation of a sphere with center at (-3, 2, 5) and a radius of 6 is:

The equation of a sphere is simply:

${(x-a)}^2+{(y-b)}^2+{(z-c)}^2=r^2$

where

$$\begin{gathered} (a, b, c) are the coordinates of the center of the sphere \\ r is the radius of the sphere \end{gathered}$$

Since we know the coordinates of the center of the sphere are (-3, 2, 5) and the radius is 6, we can write the equation of the sphere as:

$$\begin{gathered} {(x+3)}^2+{(y-2)}^2+{(z-5)}^2=6^2 \\ \mathbf{ }{\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}\mathbf{y}\mathbf{-}\mathbf{2}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}\mathbf{z}\mathbf{-}\mathbf{5}\mathbf{)}}^{\mathbf{2}}\mathbf{=}\mathbf{36} \end{gathered}$$