Find $\lim_{n\to\infty}x_n=(\frac{5\sum_{k=1}^nk^4}{n^5})^n$

sequences-and-series calculus limits

Hint: $\sum^n_{k=1} k^4 = \frac{n (n + 1) (2 n + 1) (3 n^2 + 3 n - 1)}{30}$ whence $$ \Big( \frac5{n^5}\sum^n_{k=1} k^4\Big)^n=\Big(1+\frac1n\Big)^n\Big(1+\frac{1}{2n}\Big)^n\Big(1+\frac{1}{n}\big(1-\frac{1}{3n}\big)\Big)^n$$

Can you finish from this?

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