```The `ColorFunction` of a `SphericalPlot3D` has six arguments, the first three being the \$x\$, \$y\$ , \$z\$ coodinates in \$\mathbb{R}^3\$. The fourth and fifth argument are the actual parameterization parameters of the surface and the last argument is the distance from the origin (the radius).

`#` (`Slot`) and `&` (`Function`) together allow to define anonymous function. `#4` and `#5` refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with `Function` in long form:

SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π},
ColorFunction ->
Function[
{x, y, z, u, v},
ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]]
],
ColorFunctionScaling -> False
]

Here is the example from the documentation:

GraphicsGrid[
Partition[#, 3] &@
Table[SphericalPlot3D[
1 + Sin[5 ϕ]/10, {θ, 0, Pi}, {ϕ, 0, 2 Pi},
PlotPoints -> 100,
ColorFunction ->
Function[{x, y, z, θ, ϕ, r}, Evaluate[f]],
PlotLabel -> f,
Axes -> None], {f, {Hue[x], Hue[y], Hue[z], Hue[θ],
Hue[ϕ], Hue[r]}}],

ImageSize -> Full
]

[![enter image description here][1]][1]

[1]: https://i.stack.imgur.com/fnexh.png```