Hi,
this is not a nice solution, but a slightly different approach.
Show[ParametricPlot[{Sin[n], Sin[2 n]}, {n, 0, 50}, PlotStyle -> Thin,Mesh -> #, MeshStyle -> Directive[Red]] & /@ {None, {10}} /. Point[x : {__Integer}] :> Map[Inset[Style["5", 20], #] &, x]]
and
Show[Plot[f[n], {n, 0, 2 Pi}, AspectRatio -> Automatic, Mesh -> #, MeshStyle -> Directive[Red]] & /@ {None, {10}} /. Point[x : {__Integer}] :> Map[Inset[Style["5", 20], #] &, x]]
Cheers,
Marco