Write out the first five terms of the sequence with, $\left[{\left(1-\frac{5}{n+1}\right)^{n}}\right]_{n=1}^{\infty}$, determine whether the sequence converges, and if so find its limit.

Enter the following information for $a_n=\left(1-\frac{5}{n+1}\right)^{n}$.

$a_1=$

$a_2=$

$a_3=$

$a_4=$

$a_5=$

$\displaystyle \lim_{n\to\infty} \left(1-\frac{5}{n+1}\right)^{n} =$

(Enter DNE if limit Does Not Exist.)

Does the sequence converge (Enter "yes" or "no").