The graph of
\[x^2 + 4x + y^2 - 10y + z^2 + 2z + 5 = 0\]is a sphere.  Find the center of the sphere.
Completing the square in $x,$ $y,$ and $z,$ we get
\[(x + 2)^2 + (y - 5)^2 + (z + 1)^2 = 25.\]Hence, the center of the sphere is $\boxed{(-2,5,-1)}.$