The limit of a polynomial function ($x^4-5x^2+6$) when $x$ tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term

Evaluate the limit $\lim_{x\to\infty }\left(-5x^2\right)$ by replacing all occurrences of $x$ by $\infty $

Infinity to the power of any positive number is equal to infinity, so $\infty ^2=\infty$

Any expression multiplied by infinity tends to infinity, in other words: $\infty\cdot(\pm n)=\pm\infty$, if $n\neq0$