Find the limit L $($if it exists$).$ If it does not exist, explain why. $($If an answer does not exist, enter DNE.$)$

$$lim$$x$5$f$($x$)$ where f$($x$)=$

$($x $5)2,$x $55$ x$,$x $>5$

L $=$

The limit does not exist at x $=5$ because the function value is undefined at x $=5.$The limit does not exist at x $=5$ because the function approaches different values from the left and right side of $5.$The limit does not exist at x $=5$ because the function is not continuous at any x value.The limit does not exist at x $=5$ because the function does not approach f$(5)$ as x approaches $5.$The limit exists at x $=5.$