I suspect it has something to do with [ame="http://en.wikipedia.org/wiki/Magnetic_declination"]Magnetic declination - Wikipedia, the free encyclopedia[/ame]. Orbiter shows headings based off true north, while runways are numbered off magnetic north (I think that Orbiter might actually get runway numbers wrong in things like the ILS display when the variation is large enough, but I haven't checked). For example, IRL, you should have a heading of 335 when you're pointed straight down runway 33 at KSC. In Orbiter, it shows your heading as 330. This is correct, since the variation at KSC is ~5 degrees W -- the true heading of the runway is 330, while the magnetic heading is 335.
White Sands has a variation of ~11 degrees, which fully accounts for the discrepancy you're seeing. I imagine the correct magnetic heading is around 049 (which would mean that "Runway 05" is the right name), while the correct true heading is around 060.
If the lat/long of both ends of your runway are correct, then your runway is in the correct orientation.