(21 Jun 2022, 3:47 pm)MurdnunoC wrote R5 is the Rowlands Gill/Burnopfield village service.
R3/R4 is the old 616/617 between Blaydon and Rowlands Gill via Thornley Lane & Sherburn Towers (with a varied route between Blaydon and Winlaton and a detour into Winlaton Mill). It also operates between Blaydon and Clara Vale via the old 605/606 route (more or less).
R6 is the Rowlands Gill to Winlaton via High Spen and Barlow section of the 616/617, continuing to Ryton via Stargate (I think it also goes along the Bypass and down Woodside Lane instead of going through Crookhill).
The R5 was i think what was left over after the 714/715 (Stanley - Rowlands Gill) got withdrawn.
There seemed to be a lot of M-prefixed services in these areas too, GNE operated practially all of them according to The Bygone Era