Given : Perimeter of parallelogram=$50$ cm
$\Rightarrow 50 = 2(L+B)$ $\left \{ \textbf{Perimeter of Parallelogram = 2(L+B))} \right \}$
$\Rightarrow {L+B} = {25}….(i)$
Since the length of the parallelogram is $5$ cm more than the width.
$\Rightarrow {L = B+5}….(ii)$
Put $(ii)\rightarrow(i)$ we get: $2B+5=25\Rightarrow 2B=20\Rightarrow B=10$ cm
Put $B=10$ in $(i)$ we get $L=15$ cm
Option $(A)$ is correct.