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According to the question,

$I$ varies directly as $m$ that is $I \propto m$.

Given, $I = 5$ when $m = \dfrac{2}{3}$

Now, if $m = \dfrac{{16}}{3}$, then we have to find the value of $I$

and we know that $I \propto m$

$ \Rightarrow I = km$---(1)

(Putting the value of ‘I’ and ‘m’)

$ \Rightarrow 5 = k \times \dfrac{2}{3}$

$ \Rightarrow k = \dfrac{{15}}{2}$

Now, putting the value of $k = \dfrac{{15}}{2}$ and $m = \dfrac{{16}}{3}$ in equation (1)

$ \Rightarrow I = \dfrac{{15}}{2} \times \dfrac{{16}}{3} = 40$

$ \Rightarrow I = 40$