If it has tow/haul mode, it's a 5 speed. I guess it could be possible that the wrong shift lever knob was installed, perhaps as a replacement, though I don't think that would be common. It's certainly possible, and somewhat likely, that a chassis manufactured in October of 2004 would be a 2005 model year chassis.
Seems to me you could count gears while accelerating and/or see if the button behaves as an overdrive lockout or as tow/haul. As I understand things, if you're going down a flat highway section (in overdrive) and activate tow/haul, it should not generally downshift immediately, while of course if it's locking out overdrive it will downshift.
