Answer
$$2.5$$
Work Step by Step
We need to find $$\lim _{\theta \rightarrow 0} \frac{\sin 5 \theta}{\sin 2 \theta}$$
Consider the function $$ f(\theta)= \frac{\sin 5 \theta}{\sin 2 \theta}$$
From the following figure, we can observe that
\begin{align*}
\lim _{\theta \rightarrow 0^+} f( \theta)&=2.5\\
\lim _{\theta \rightarrow 0^-} f( \theta)&=2.5
\end{align*}
Since the left and right limits equal each other, we can say that $$\lim _{\theta \rightarrow 0} \frac{\sin 5 \theta}{\sin 2 \theta}=2.5 $$
