With 56038. Apparently photos of D5511 on trial anywhere in Scotland in 1958 are like hen's teeth. The date must be after June 18th, because that is when the RO reports it as being seen going north towards Perth.

Alistair Moffat adds "D5511 visited the Highland main line, Inverness to Aberdeen line, Far North/ Kyle at least to Dingwall, West Highland to Mallaig, Callander and Oban, and the Waverley route through Hawick to Carlisle. All in the late summer of 1958, July and August."