It certainly started out as a Log Branch No.4Mk1*. The buttstock is No.4 and I think the original No.4 forestock was cut back and the metal cap of its forend reused on the shortened forestock. The grooves on the handguard (top wood of the forestock) are consistent with some rear handguards (in that position) on No.4, usually Savage production but certainly some were supplied to LongBranch. I think it has been modified to fit the modified forestock to look like a No.5, as others have said.
The foresight isn't No.4, and if it's No.1 it has a protector that isn't from any Enfield I have seen. I think the original No.4 barrel has been shortened (no bayonet lugs or sight mount) and a non-standard foresight installed.