Limit to infinity part 2

$\lim_{x \to \infty} \frac{(n^5 + 5n^4 + ...) + (n^5 + 10n^4 + ...) + ... + (n^5 + 50n^4 + ...) - 10n^5}{n^4} = \\\\\\ \lim_{x \to \infty} \frac{\cancel{10n^5} + 275n^4 + ... - \cancel{10n^5}}{n^4} = \\\\\\ \lim_{x \to \infty} = \frac{n^4(275 + \frac{p}{n} + \frac{q}{n^2} + ...)}{n^4} = \\\\ 275 + 0 = \\\\ \boxed{\boxed{275}}$

Obs.: $\forall \, p, q \in \mathbb{N}$ .

Just apply the binomial expansion

The above hint is more than enough