(a) The positive sequence \(u_1,u_2,u_3,\ldots\) satisfies \(u_1<5\) and \(u_{n+1}=\dfrac{6u_n+5}{u_n+2}\). By considering \(5-u_{n+1}\), prove by induction that \(u_n<5\) for all positive integers \(n\).

(b) Show that \(u_{n+1}>u_n\) for \(n\ge1\).