[If anyone can give me more information on this gun (in particular the scope)]
The Winchester A5 scope was introduced in America in 1909 and remained in production until 1928 , some 3200 in toto - it was a long-term favourite of target rifle shooters.
It is 16" long and 0.75" in diameter, with a steel tube, 5x magnification and external ½MOA elevation/windage adjustments.
Most specified a crosshair reticle but a few with single crosshair examples are known to exist along with a handful of the slightly shorter 4x magnification Winchester B4 scopes.
The scopes mounted on service rifles sometimes had the rifle's serial number engraved on the side of the steel tube.
One of the Winchester A5's drawbacks compared to other scopes was that it was somewhat fragile: it could easily be knocked out of zero.
It also had a narrow field of view; lower light gathering capability which restricted its use at dawn and dusk; and a requirement to pull it back into battery after each shot because the scope moved forward in recoil.
Lastly, the external surface of the tube had to be kept scrupulously clean in order for the external adjustments to work properly and consistently.
Despite these faults it was a popular and accurate scope, praised for its easy windage and elevation adjustments.