Leigh was clearly not afraid to have even her beginner students get used to playing in irregular time signatures. In this case, the 5/4 signature is necessary in order to correctly represent the call of the wood pigeon.
The piece may well reference a famous local story of Jimmy Wells, who supposedly blew his arm off when shooting pigeons off his cottage roof. However this clipping from the Monmouthshire Beacon on 8th January 1897 claims that Wells actually shot his friend, Ryder. Whilst David Ryder was indeed a local man and a companion of Wells, I can find no other accounts that claim it was anybody other than Wells who was injured. In addition, a tune entitled "Watch Where You're Shooting, Jimmy Walls" is contained amongst the Seaton Snook Northumbrian Smallpipe Tunes, and which also contains a phrase mimicking the call of the wood pigeon.