plot – How to plot discontinuous iterated 3D plot?

I'm having trouble drawing this data set

triples = {{0, 1, 1}, {9/50, 4/5, 1}}, {{9/50, 4/5, 1}, {3/8, 4/5, 1}}, {{3/8, 58333/100000, 1}, {3/4, 16667/100000, 1}}, {{3/4, 0, 1}, {1, 0, 1}}, {{0, 1, 2}, {27/100, 4/5, 2}}, {{27/100, 4/5, 2}, {9/16, 4/5, 2}}, {{9/16, 0, 2}, {1, 0, 2}},
{{0, 1, 3}, {81/200, 4/5, 3}}, {{81/200, 4/5, 3}, {21/32, 4/5, 3}}, {{ 21/32, 0, 3}, {1, 0, 3}},
{{0, 1, 4}, {243/400, 4/5, 4}}, {{243/400, 0, 4}, {1, 0, 4}}, {{0, 1, 5} , {471/800, 43539/50000, 5}}, {{471/800, 0, 5}, {1, 0, 5}}

At first I had pairs of points, after having added the third coordinate to be able to plot it in 3D, but the problem now is that I can not trace it, because each iteration is given by linear parts by parts, by intervals.
I would like to obtain a 3D graph of this set of points, where each z coordinate is an iteration.

For the layout I use this

Show[ListPointPlot3D[triples, AxesLabel -> {x, y, z},
PlotRange -> {{0, 1}, {0, 1}, {0, 5}}, ColorFunction -> “Rainbow”,
BoxRatios -> {1, 1, 2}], Graphics3D[Line[triples]]]

but it gives me an error:> The settings specified for the Graphics3DBoxOptions, PlotRange option can not be used.

Any suggestion would be greatly appreciated.