Answer
$\sinh x= \dfrac{4}{3}$
Work Step by Step
As we are given that $ x \gt 0$, so $\sinh x = \sqrt{ (cosh^{2}x - 1)}$
Plug $\cosh x = \dfrac{5}{3}$
Thus, $\sinh x =\sqrt{ (\frac{5}{3}^{2}-1)}$
or, $=\sqrt {\dfrac{25}{9}-1}$
or, $=\sqrt{ \dfrac{25-9}{9}}$
or, $=\sqrt {\dfrac{16}{9}} $
or, $= \dfrac{4}{3}$
