The diagram shows part of the curve

\(y=x+e^{5-2x},\)

the normal to the curve at the point \(A\), and the line \(x=5\). The normal to the curve at \(A\) meets the \(y\)-axis at the point \(B\). The \(x\)-coordinate of \(A\) is \(2.5\).

(i) Find the equation of the normal \(AB\).

(ii) Showing all your working, find the area of the shaded region.