```The `ColorFunction` of a `SphericalPlot3D` has five arguments, the first three being the \$x\$, \$y\$ , \$z\$ coodinates in \$\mathbb{R}^3\$. The _last two_ are the actual parameterization parameters of the surface.

`#` (`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
]

Compare this also to the following:

g = GraphicsRow[
Table[
SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π},
PlotPoints -> 100,
ColorFunction -> f
],
{f,
{
Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi x])/2]],
Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi y])/2]],
Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi z])/2]],
Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi u])/2]],
Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi v])/2]]
}
}
],
ImageSize -> Full
]

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

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