Color ParametricPlot3D with three colors

I can color a helix with 2 colors:

ParametricPlot3D[{Sin[t], Cos[t], t/3}, {t, 0, 15}, 
 ColorFunction -> Function[{x, y, z, t}, If[t < 5, Red, Green]], 
 ColorFunctionScaling -> False]

But I can’t figure out how to color with 3 colors, say, t < 5 red, 5<=t<=10 green, t>10 blue.

Instead of If[t < 5, Red, Green], it could be Piecewise[{{Red, t < 5}, {Green, 5 <= t <= 10}, {Blue, t > 10}}] .

ParametricPlot3D[{Sin[t], Cos[t], t/3}, {t, 0, 15}, 
 ColorFunctionScaling -> False, 
 ColorFunction -> 
  Function[{x, y, z, t}, 
   Piecewise[{{Red, t < 5}, {Green, 5 <= t <= 10}, {Blue, t > 10}}]]]

I got it! Thank you very much.