I have no idea what I'm doing wrong. Ideas?
Interchange a couple of rows, and finish up the elimination.
Can take the third and fifth unknowns free.
I believe you must have already done this.
So if you're saying {v_1, v_2} is your basis for Null(A), then I don't see what's wrong.
EDIT: I wasn't aware of the preceding post until after I made mine.
Anyway, the two vectors you obtained are exactly the two that I obtained by simply doing what I suggested above.