Answer
Yes. No
Work Step by Step
Because A has a pivot in each row, its columns span $R^3$ so $Col\ A = R^3$. However, because Nul A is a subspace of $R^5$, it can't equal $R^2$. However, because the equation $Ax=0$ has 2 free variables and A has 5 columns and 3 pivot columns, the dimension of Nul A is 2.
