Your odds would be slightly better, only because I have the chance of certain combos being picked more than once. Of course, that being the case, the overall expected return is the same, b/c I could hit the same 5/5 twice or more in those rare instances.
BTW, I do pick my own numbers when I play. That's only because I think it's more fun, and because I can slightly raise expected value by picking combos that are less likely to be picked by other players (using a larger amount numbers higher than 31, b/c many self pick players use dates for their picks.)
As for their odds of being drawn, I think a QP is just the same as any self pick. The difference with buying large amounts of QPs is there, but negligible unless you really started buying millions....
I figured it'd be easy if I was able to use a set of RNGed numbers, the same amount you were picking for 2 reasons...
1) I'm not influencing the decision, except to insure that I don't have the same set of numbers twice.
2) I wouldn't have to go through much trouble to do this. I've got other things I'm far more focused on (working on poker tournament play for an upcoming trip - and I'm taking a Winter class that I know I'm going to have trouble with)
If you don't want that challenge, it's fine. If nobody else takes you up, you can still run the test yourself.