A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3.

Let the length and breadth of the rectangular lawn be 5x m and 3x m, respectively.

Given:

Area of the rectangular lawn $=3375 \mathrm{~m}^{2}$

$\Rightarrow 3375=5 x \times 3 x$

$\Rightarrow 3375=15 x^{2}$

$\Rightarrow \frac{3375}{15}=x^{2}$

$\Rightarrow 225=x^{2}$

$\Rightarrow x=15$

Thus, we have:

$l=5 x=5 \times 15=75 \mathrm{~m}$

$b=3 x=3 \times 15=45 \mathrm{~m}$

Perimeter of the rectangular lawn $=2(l+b)$

$=2(75+45)$

$=2(120)$

$=240 \mathrm{~m}$

Cost of fencing 1 m lawn = Rs 65

$\therefore$ Cost of fencing $240 \mathrm{~m}$ lawn $=240 \times 65=\mathrm{Rs} 15,600$