Answer
a:
$\lim\limits_{x \to \infty}f(x)=5$ says: as x gets infinitely large positively, a horizontal asymptote forms at $y=5$
b:
$\lim\limits_{x \to -\infty}f(x)=3$ says: as x gets infinitely large negatively, a horizontal asymptote forms at $y=3$
Work Step by Step
a:
$\lim\limits_{x \to \infty}f(x)=5$ says: as x gets infinitely large positively, a horizontal asymptote forms at $y=5$
b:
$\lim\limits_{x \to -\infty}f(x)=3$ says: as x gets infinitely large negatively, a horizontal asymptote forms at $y=3$