Air Carrier Captain reported the RNP Runway 5 approach to RDU '...brings you in well left of runway centerline...'. The reporter has experienced this several times in different aircraft.

Narrative

I just wanted to bring something to your attention that is a potential safety issue associated with the RNP 5L in RDU. I have been working RDU flights all month and the first couple of times that I flew this approach I thought that it was my flying skill; but after having done this all month I can safely say that it is how the approach is built. When arriving into RDU; I have been requesting this approach via the HEAVE transition which dumps you off the ALDAN STAR onto the RNP approach course. The LNAV portion of this particular approach brings you in well left of runway centerline; so much so that if you do not make any corrections when crossing the threshold; the right mains will also touchdown well left of centerline. I have flown this approach several times this month in 800s; and two other aircraft types which leads me to believe that this is how the actual approach is built. I have triple checked the RNP values several times and the aircraft has always been performing within RNP requirements. I have also flown the RNP 23R and that approach works as it should. Nothing additional to include. Reevaluate the RNP 5L approach course.