Point on a line closest to the origin

On my last calc test, they asked f(x)=10x+5, what point in the function is closest to the origin?

I solved it by finding the normal line which intersects the origin, then finding where that line intersects f(x). (We haven't gotten the tests back yet, so I don't know how if that worked)

Anyway, this didn't involve any calculus, so I'm concerned that the problem was written wrong, and was supposed to be something like $\displaystyle 10x^{3}+5$.

This question, I am not sure how to solve, so can anyone help me figure out how I would find the point on the function $\displaystyle f(x)=10x^{3}+5$ which is closest to the origin?

And if this method does not require normal lines, could you also explain to me how I would find the normal line for such a function? (I have a theory that it would be $\displaystyle -\frac{1}{30x^{2}}$ but that's just a theory.)