5 The region bounded by the \(x\)-axis, the \(y\)-axis, the line \(x = \ln 5\) and the curve \(y = \mathrm { e } ^ { x }\) for \(0 \leqslant x \leqslant \ln 5\), is occupied by a uniform lamina.
- Show that the centre of mass of this lamina has \(x\)-coordinate
$$\frac { 5 } { 4 } \ln 5 - 1$$
- Find the \(y\)-coordinate of the centre of mass.