Determine the following limits$,$ using $\backslash$infty or $-\backslash$infty when appropriate, or state that they do not exist.

Given expressions:

a$.$

$\backslash$lim$\_\{$x $\backslash$to $5^-\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}$

b$.$

$\backslash$lim$\_\{$x $\backslash$to $5^+\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}$

c$.$

$\backslash$lim$\_\{$x $\backslash$to $5\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}$

a$.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\backslash$lim$\_\{$x $\backslash$to $5^-\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}=\backslash$boxed$\{\backslash$phantom$\{$answer$\}\}$

B$.$ The limit does not exist and is neither $\backslash$infty nor $-\backslash$infty

b$.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\backslash$lim$\_\{$x $\backslash$to $5^+\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}=\backslash$boxed$\{\backslash$phantom$\{$answer$\}\}$

B$.$ The limit does not exist and is neither $\backslash$infty nor $-\backslash$infty

c$.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\backslash$lim$\_\{$x $\backslash$to $5\}\backslash$frac$\{$x$^2-7$x $+12\}\{($x $-5)^2\}=\backslash$boxed$\{\backslash$phantom$\{$answer$\}\}$

B$.$ The limit does not exist and is neither $\backslash$infty nor $-\backslash$infty