Find the first five terms of the sequence. \[ \begin{array}{l} a_{n}=n^{n} \\ a_{1}=\square \\ a_{2}=\square \\ a_{3}=\square \\ a_{4}=\square \\ a_{5}=\square \end{array} \] Determine whether the sequence is geometric. If it is geometric, find the common ratio $r$. (If the sequence is not geometric, enter DNE.) $r=$ Express the $n$th term of the sequence in the standard form $a_{n}=a r^{n-1}$. (If the sequence is not geometric, enter DNE.)

Step 1 ：The sequence is defined by the formula \(a_n = n^n\).

Step 2 ：To find the first five terms, we substitute \(n = 1, 2, 3, 4, 5\) into the formula, yielding the terms 1, 4, 27, 256, and 3125.

Step 3 ：A sequence is geometric if the ratio of any two consecutive terms is constant. We calculate the ratio of \(a_{n+1}/a_n\) for the first few terms and find that they are not constant.

Step 4 ：Therefore, the sequence is not geometric, and the common ratio and the nth term in standard form do not exist.

Step 5 ：Final Answer: The first five terms of the sequence are \(\boxed{1, 4, 27, 256, 3125}\). The sequence is not geometric, so the common ratio is \(\boxed{\text{DNE}}\) and the nth term in standard form is \(\boxed{\text{DNE}}\).