Answer
$ \bf{Not \ Orthogonal}$
Work Step by Step
When the dot product of two vectors becomes zero, the vectors are said to be orthogonal, for this we will multiply the corresponding components together and then adding .
In general, we have the formula as: $ a \cdot b =a_1 b_1+a_2b_2$
Now, we have $a \cdot b=\lt \sqrt 5, -2 \gt \cdot \lt -5, -2 \sqrt 5 \gt =(-5)(\sqrt 5)+(-2)(-2 \sqrt 5)=-5\sqrt 5 +4 \sqrt 5=-\sqrt 5$
Therefore, the two vectors are $ \bf{Not \ Orthogonal}$ .