Answer
the vectors of $S$ are not linearly independent.
Work Step by Step
The set $S=\{(-4,5),(0,0)\}$ is not a basis for $R^2$ because the vectors in $S$ are not linearly independent. Indeed, considering the linear combination
$$c_1 (-4,5)+c_2(0,0)=(0,0),$$
then the choice $c_1=0$ and any non-zero value for $c_2$ satisfies the above combination. Hence, the vectors of $S$ are not linearly independent.