$\frac{10}{3}: x:: \frac{5}{2}: \frac{5}{4}$ is of the form $a: b:: c: d$
i.e $\frac{10}{3} \times \frac{5}{4}=x \quad \times \frac{5}{2}$
$x=\frac{\frac{10}{3} \times \frac{5}{4}}{\frac{5}{2}}$
$x=\frac{10}{3} \times \frac{5}{4} \times \frac{2}{5}$
$x=\frac{5}{3}$