The curve \(C\) has equation
\(y=\frac{5 x^{2}+5 x+1}{x^{2}+x+1} .\)
(i) Find the equation of the asymptote of \(C\).

(ii) Show that, for all real values of \(x,-\frac{1}{3} \leqslant y\lt 5\).

(iii) Find the coordinates of any stationary points of \(C\).

(iv) Sketch \(C\), stating the coordinates of any intersections with the \(y\)-axis.