I had a look through Skennertons latest one on the Lee Enfield I have all his books on the Lee Enfield (from 1st to last including a No.30 signed Presentation copy which makes 4 books) there is nothing on any No5's being approved for Skeletonisation in those books.
Marks/Dates for approvals were ~ No.4 Mk I & Mk I*, 11.12.50 & No4 Mk 1/2, 1/3 & 2, 03/02/1955 there was nothing in Strattons book either.
Though there may have been different workshops for reasons unknown may have done them but as PL would say it probably was not in the EMER's say during the war but as we have learnt here never say never with enfields.....