Wouldn't this need to be in the conditional mood? Or is it? Is the conditional mood even in the course? I'm really questioning my thought process right now.
In English, the conditional is often used simply for politeness, not indicating a condition.
So this question is not conditional ("Would you like to dance with me if ....?") but simply a more polite version of "Do you want to dance with me?".
So it doesn't have to be conditional in Turkish.
(Conditional is in the course -- the -sA ending.)
That's where I was confused. Since it wasn't conditional, I wrote "do you want to dance with me?" which was marked incorrect. It was because of this that I assumed that it HAD to be conditional since it only accepted "would you..."