Does the sequence $\{a_n\}$ converge or diverge? Find the limit if the sequence is convergent.

$a_n=\frac{3+2n^4}{n^4+5n^3}$

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

A$.$ The sequence converges to $\underset{n}{lim}{a}_n=.($Simplify your answer.$)$

B$.$ The sequence diverges.