order=50;
a=5.0;
f[x_]:=(1+x)^(2/3);
c[n_]:=1.0*(D[f[x],{x,n}]/.{x->a})/n!;
p=Sum[c[k]*(x-a)^k,{k,0,order}];
Plot[{p,f[x]},{x,-5,15},PlotStyle->{Thin,{Thick,Dotted}}]