X={2v+(1+(v^2))Cos[u]+4(1+(v^2))Sin[u],v+2(1+(v^2))Sin[u],v+(1+(v^2))Sin[u]};

norm[x_]:=(Sqrt[x.x])

nn=((((∂_u)X\[Cross](∂_v)X)/(norm[(∂_u)X\[Cross](∂_v)X]))//Simplify)

f1={α,β}/.Solve[(∂_u)nn==α (∂_u)X+β (∂_v)X,{α,β}][[1]];
f2={α,β}/.Solve[(∂_v)nn==α (∂_u)X+β (∂_v)X,{α,β}][[1]];

k=(Det[{f1,f2}]//Simplify)

(Solve[D[k,{{u,v},1}]=={0,0}]//N)/.{(C[1])->0,(C[2])->0}

k/.%

Select[%,Im[#]==0&]

Max[%]

Therefore, the correct option is 5).