Answer
converges to $5$
Work Step by Step
Since, $ \lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (3^n +5^n)^{1/n}$
This implies that $ 5 \lim\limits_{n \to \infty} [(\dfrac{3}{5})^n+1]^n=5(1)=1$
Thus, $\lim\limits_{n \to \infty} a_n=5$ and {$a_n$} converges to $5$.
