Die is thrown $5$ times. $\therefore \:n=5$

$P(X=$odd no comes exactly 3 times) $=P(X=3)$

We know that $P(X=r)=^n C_r p^r q^{n-r}$

$\Rightarrow\:P(X=3)=^5C_3\;(\frac{1}{2}\;)^3\;(\frac{1}{2}\;)^2$

$=10\times\large(\frac{1}{2^5})$

$=\large\frac{5}{16}$