Answer
$\dfrac{5}{2}$
Work Step by Step
Consider: $\lim\limits_{t \to 0}f(t)=\lim\limits_{t \to 0}\dfrac{\sin (5t)}{2t}$
Need to check that the limit has an indeterminate form.
Thus, $f(0)=\dfrac{\sin (5(0))}{2(0)}=\dfrac{0}{0}$
Now, apply L-Hospital's rule such as: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$
This implies:
$\lim\limits_{t \to 0}\dfrac{(5) \cos 5t}{2}= \lim\limits_{t \to 0}\dfrac{ 5 \cos 0}{2}=\dfrac{5}{2}$
