Evaluate the following limit or explain why it does not exist.

ModifyingBelow lim With x right arrow infinitylimx$$left parenthesis $1$ plus StartFraction $5$ Over x cubed EndFraction right parenthesis Superscript x cubed$1+5$x$3$x$3$

Question content area bottom

Part $1$

Select the correct choice$$ and, if$$ necessary, fill in any answer boxes to complete your choice.

A$.$

Lequals$=$ModifyingBelow lim With x right arrow infinitylimx$$x cubed ln left parenthesis $1$ plus StartFraction $5$ Over x cubed EndFraction right parenthesisx$3$ln$1+5$x$3$

is finite and therefore

ModifyingBelow lim With x right arrow infinitylimx$$left parenthesis $1$ plus StartFraction $5$ Over x cubed EndFraction right parenthesis Superscript x cubed$1+5$x$3$x$3$

can be written as the expression

enter your response here.

$($Type an expression using L as the$$ variable.$)$

This implies that

ModifyingBelow lim With x right arrow infinitylimx$$left parenthesis $1$ plus StartFraction $5$ Over x cubed EndFraction right parenthesis Superscript x cubed$1+5$x$3$x$3$equals$=$e Superscript $5$e$5.$

$($Type an exact answer in simplified$$ form.$)$