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

You can make usage of `DensityPlot3D` that gives you 4D plotting (3 axes and 4th color variable) and then run remaining 5th variable through a range of values. This code will give you the top image (explore options of `DensityPlot3D` to adapt to your needs):

    Multicolumn[
    Table[
    DensityPlot3D[
    	Cos[Pi a]Cos[Pi b]+Cos[Pi g]Cos[Pi d],
    	{a,0,1},{b,0,1},{g,0,1},
    	PlotLabel->"d = Pi*"<>ToString[N[d,2]],
    	ColorFunction->"TemperatureMap",
    	PlotTheme->"Detailed",
    	PlotLegends->None],
    {d,0,1,1/15}]
    ,4]


  [1]: https://i.sstatic.net/vnkAL.jpg