Answer
Converges to $5$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (3^n +5^n)^{1/n}$
Since, $ \lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$
So, $ \lim\limits_{n \to \infty} 5((\dfrac{3}{5})^n+1)^n=5$
Hence, $\lim\limits_{n \to \infty} a_n=5$ and {$a_n$} is Convergent and converges to $5$
