2.24: Normal and shaded area for an exponential curve

The diagram shows part of the curve $y = x + \mathrm{e}^{5 - 2x}$, 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 $2.5$.