Direct substitution

If substitution gives a number, that number is the limit and you are finished. If it gives an indeterminate form, the attempt has told you which technique to reach for next rather than wasted your time.

A result like $\frac{5}{0}$ is not indeterminate: it tells you the limit is not a finite number. Check each one-sided limit, which will be $+\infty$ or $-\infty$. If the two sides agree the limit is infinite with that sign, and if they disagree, as in $\lim_{x \to 0} \frac{5}{x}$, the two-sided limit does not exist.