It sounds like it could have been a "homemade" copy of a Jungle Carbine. They were a No. 5, not a Mk5.
The No. 1 MkIII (etc) were the pre WWII version with open barrel mounted open sights. The No.4 MkI (etc) series and the No. 5 Jungle Carbine had receiver mounted peep sights.
The Jungle Carbine came into service late in the war, and then in very limited numbers. As far as I know none of them (Jungle Carbines) were made by Savage, however I know the No. 4's were because I have one so marked.