Find the angle subtended at the centre of a circle of radius

We know that the arc length l of a sector of an angle θ in a circle of radius r is

$l=\frac{\theta}{360^{\circ}} \times 2 \pi r$

It is given that $r=5 \mathrm{~cm}$ and length $l=\frac{5 \pi}{3} \mathrm{~cm}$. Substituting these value in above equation,

$\frac{5 \pi}{3}=\frac{\theta}{360^{\circ}} \times 2 \pi \times 5$

$5 \pi \times 360^{\circ}=\theta \times 2 \pi \times 5 \times 3$'

$\theta=60^{\circ}$

Hence, the angle subtended at the centre of circle is $60^{\circ}$.