#### Answer

arithmetic sequence
$a_5=5\sqrt{2}$

#### Work Step by Step

We are given:
$\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}$, ...
We can see that this is an arithmetic sequence because the values go up consistently by $d=\sqrt{2}$.
Thus the 5th term is:
$a_5=a_4+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}$