Answer
$5$
Work Step by Step
\begin{align*}
\lim _{\theta \rightarrow 0} \frac{ \sin 5\theta}{ \theta}&=5\lim _{5\theta \rightarrow 0} \frac{ \sin 5\theta}{5\theta}\\
&=5(1)=5
\end{align*}
Where we used, $\lim _{x\rightarrow 0}\frac{ \sin x}{ x}=1. $
