5 A curve \(C\) has parametric equations
$$x = \frac { 2 } { 5 } t ^ { \frac { 5 } { 2 } } - 2 t ^ { \frac { 1 } { 2 } } , \quad y = \frac { 4 } { 3 } t ^ { \frac { 3 } { 2 } } , \quad \text { for } 1 \leqslant t \leqslant 4$$
- Find the exact value of the arc length of \(C\).
- Find also the exact value of the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.