Not so crystal.
I do not think mothergoose1 understands fully the technology behind MCDU BACK-UP NAV.
Originally Posted by FCOM DSC-22_30-30 B AP Engagement
In BACK–UP NAV, AP can be engaged in selected modes if the FG part is available.
So, AP yes, RNAV yes-some. The whole feature as far as I understand it was developed to increase redundancy for ocean crossings, keeping the RNP capability as a sole objective.
Specifically about RNP5, I do not know. RVSM no problem.