PlotStyle according to PlotRange

You could do as in the link J.M. provided, define the plotted function as a piecewise function. But you can make a custom piecewise color function,

regions = {"0≤θ<π/3", 
   "π/3≤θ<2π/3", 
   "2π/3≤θ<π", 
   "π≤θ<4π/3", 
   "4π/3≤θ<5π/3", 
   "5π/3≤θ<2π"};
colors = {Red, Blue, Green, Orange, Pink, Magenta};

colorfunc[θ_] = 
  Piecewise[Transpose[{colors, ToExpression /@ regions}]];

and then use that on your plot. Here I'm feeding colorfunction the value #3 which is the value of theta (I think #1 and #2 would be x and y). Far as I can tell, the

ParametricPlot[Hypocycloid[{5, 1}, θ], {θ, 0, 2 Pi},
 ColorFunction -> (colorfunc[#3] &),
 ColorFunctionScaling -> False,
 Axes -> None, Frame -> True, PlotRange -> All,
 PlotLegends -> SwatchLegend[colors, regions]]