Taking a different track, that scoped No5 has been made up in the past from a written off/scrap Lyman TP No4 in the days of plenty. I expect that in the near future the Lyman scope, bracket and body mount will find themselves mated up to a 'suitably marked' No4 and emerge thereafter as a genuine No4 TP. The unsuspecting will fall for it but hopefully, the knowing will be fore-armed, using the info that they've gleaned from this site.
As I say and have said many times. It's EASY putting a telescope onto a rifle. It's much HARDER putting a telescope onto a rifle optically and mechanically correctly.
As a matter of interest, in the 90's or so we rebarrelled our No4TP and what a palava................. The barrel was badly pitted so a new F55 barrel (still original or what............) was fitted. The body mount wouldn't allow the use of the body and barrel clamp/spanner so that had to come off. Once it was replaced and sweated on, true to form, the optical axis if the telescope didn't align with the new barrel bore and the tapered locating pegs made any notion of fine adjustment impossible. I did it but what an effort