Firstly I know that this has been discussed in other threads but hear me out.
Now according to the core rulebook,
"If you have a base attack bonus of +1 or higher, you may draw a weapon as a free action combined with a regular move."
Now I understand that there was some debate as to what "a regular move" really meant, and in a lot of the threads they seemed to classify it as actually moving your character (like in feet) as part of a move action. But if you look at the quickdraw feat, near the end it says, "Without this feat, you may draw a weapon as a move action, or (if your base attack bonus is +1 or higher) as a free action as part of movement."
So here in the book it just classifies the prerequisite as just "movement" and if you look under 5-foot step it says, "You can move 5 feet in any round when you don't perform any other kind of movement." Since it says 'any other' this would mean that the book classifies a 5-foot step as "movement"
So would I be able to draw a weapon as part of a 5-foot step with a BAB +1?