Perimeter = 480 m
ratio of length and breadth = 5 : 3
$\begin{align*}\text{Let the length} & = 5x \\ breadth & = 3x \\ Perimeter & = 2(l + b) \\ 2(5x + 3x) &= 480 \\ 2(8x)& = 480 \\ 8x & = \frac{480}{2} \\ 8x &= 240 \\ x& = \frac{240}{8} \\ x& = 30 \end{align*} $
$\implies length = 5 \times 30 = 150$
$breadth = 3 \times 30 = 90$
$\begin{align*} Area & = 150 \times 90 \\ & = 13500m^2\end{align*}$