Answer
$$1$$
Work Step by Step
We are given $$g(t)=5^{-1 / t^{2}} $$
We find the limit of the exponent:
\begin{align*}
\lim _{t \rightarrow \pm \infty}-\frac{1}{t^{2}}&=-\frac{1}{\infty}\\
&=0
\end{align*}
Then
\begin{align*}
\lim _{t \rightarrow \pm \infty} 5^{-1 / t^{2}}&=5^{\lim _{t \rightarrow \pm \infty} -\frac{1}{t^{2}}}\\
&=5^{0}=1
\end{align*}
