\[\begin{split} &\lim_{n \to \infty} \frac{5n^6-3n^4+2}{5-9n^6}=\\[15pt] &=\lim_{n \to \infty} \frac{5n^6-3n^4+2}{5-9n^6}\ \frac{:n^6}{:n^6}=\\[15pt] &=\lim_{n \to \infty} \dfrac{\dfrac{5n^6}{n^6}-\dfrac{3n^4}{n^6}+\dfrac{2}{n^6}}{\dfrac{5}{n^6}-\dfrac{9n^6}{n^6}}=\\[15pt] &=\lim_{n \to \infty} \dfrac{5-\dfrac{3}{n^2}+\dfrac{2}{n^6}}{\dfrac{5}{n^6}-9}=\\[15pt] &=-\frac{5}{9} \end{split}\]