Find the limit$.$

$\underset{x4}{lim}\frac{\sqrt[\phantom{2}]{x^2+9}-5}{x-4}$

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

A$.\underset{x4}{lim}\frac{\sqrt[\phantom{2}]{x^2+9}-5}{x-4}=($Type an integer or a simplified fraction.$)$

B$.$ The limit does not exist.Find the limit$.$

$\underset{x4}{lim}\frac{\sqrt[\phantom{2}]{x^2+9}-5}{x-4}$

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

A$.\underset{x4}{lim}\frac{\sqrt[\phantom{2}]{x^2+9}-5}{x-4}=($Type an integer or a simplified fraction.$)$

B$.$ The limit does not exist.