Hope u can reach this step
(n^5/5 - 1/5) (n^6/6 - 1/6) / [ (n^t+1/t+1 - 1/t+1 )(n^10-t/10-t - 1/10-t)]
\lim_{n\rightarrow \infty}\frac{(\sum_{x=1}^{n}{x^4})(\sum_{x=1}^{n}{x^5})}{(\sum_{x=1}^{n}{x^t})(\sum_{x=1}^{n}{x^{9-t}})}=\frac{4}{5}
Hope u can reach this step
(n^5/5 - 1/5) (n^6/6 - 1/6) / [ (n^t+1/t+1 - 1/t+1 )(n^10-t/10-t - 1/10-t)]