Evaluate the following limits and identify the horizontal asymptotes (if any) for the function $f\left(x\right)=\frac{5x}{25x+3}$:
${\lim }_{x\to \infty }f\left(x\right)$
${\lim }_{x\to -\infty }f\left(x\right)$

${\lim }_{x\to \infty }f\left(x\right)$ $=\frac{1}{5}$

${\lim }_{x\to -\infty }f\left(x\right)$ $=\frac{1}{5}$

Horizontal asymptote: $y=\(\frac\)15$

${\lim }_{x\to \infty }f\left(x\right)$ $=\frac{1}{5}$

${\lim }_{x\to -\infty }f\left(x\right)$ $=-\frac{1}{5}$

Horizontal asymptotes: $y=5$ and $y=-5$

${\lim }_{x\to \infty }f\left(x\right)$ $=\frac{1}{3}$

${\lim }_{x\to -\infty }f\left(x\right)$ $=-\frac{1}{3}$

Horizontal asymptotes: $y=3$ and $y=-3$

${\lim }_{x\to \infty }f\left(x\right)$ $=\frac{1}{3}$

${\lim }_{x\to -\infty }f\left(x\right)$ $=\frac{1}{3}$

No horizontal asymptote