Answer
$$\|v+w\|= \sqrt{10}.$$
Work Step by Step
Since $ v=\langle -2,5\rangle $ and $ w=\langle 3,-2\rangle $, then we have
$$ v+w=\langle -2,5 \rangle+\langle 3,-2 \rangle =\langle 1,3 \rangle.$$
Hence, the length of $ v+w $ is given by
$$\|v+w\|=\sqrt{1^2+3^2}=\sqrt{10}.$$
