Small correction if I may.

I don't know of a MK1 No5.

There was a No5, Mk1, a.k.a. the "jungle Carbine(sic)".

I know it sounds petty, but it isn't there are No3 Mk1s & No1 MkIIIs and they're different rifles.

They had nothing to do with Jungles for a start. That was a post WW2 marketing moniker. The real purpose was for a lighter, handier rifle for things like urban warfare.

They were made by only 2 factories. Birmingham Small Arms & Royal Ordinance Factory, Fazakerly.

If you have a full sized SMLE/No1 MkIII or No 4 rifle stick a bayonet on it & the try to maneuver round inside your home (warn the wife & kids First though ).

There was a phase for wanting them because they were "way more kewl than a full sized rifle" & they commanded a bit of a premium if unmolested. Many were.

This meant it was worth while faking one by chopping down a No4. & making a faux carbine to flip it for a higher price.

The truth is they were more finicky, slightly less accurate, You'll come across horror stories of the "Wandering Zero" a problem with the sighting varying in an unexplained way. Let me clear the air for you a bit on this.

Yes, It did exist.

No, It wasn't all the rifles.

Any showing the defect were returned for repair & were either repaired, or scrapped as "Unfit For Service". There was a kind of evolution involved, survival of the fittest.

Some do still exist, but most either were fixed or scrapped so you probably don't have one, but you might.

If you send us some pictures (look down in info for new owners for help with this) we'll know more about YOURS & can be more helpful & more specific.

Oh, welcome aboard!

Here's a quick 'n dirty How to tell a real one from a fake image set.

No5s were ONLY made by BSA & Fazakerly, if the serial number goes to any other ROF its fake!
"Who Made My Lee Enfield
First digit of serial number
1-= Maltby
2- = Fazakerly
3-= BSA Shirley
OC1- Savage
OL1- Long Branch

Or:
All factories in the North were prefixed with a "N", those in the Midlands were prefixed by "M" and those in the South prefixed by "S"
BSA (Birmingham Small Arms)
M47A = Small Heath (Nr Birmingham)
M47B = 3 small assembly plants at Redditch, Hereford and Worcester
M47C = The main factory at Shirley (district in Birmingham)

OR
To work out which factory that your No4 was made is to look at wrist markings where the serial numbers are. Now this only equates to British No4MkI here. The British made No4MkI’s use a prefix and number – (Alpha numerical) system to identify manufacturer. Numbered serials starting with 1 indicated ROF Maltby, 2 indicated ROF Fazakerley and 3 indicated BSA Shirley. However as one soon learns with anything to do with life there are exceptions, early in on the game BSA Shirley did a production run which used only 4 numbers and went from Axxxx to Zxxxx."

note that the no5s were only made at BSA or FAZAKERLY - origins 

the BSAs are marked with the M47 on left wrist , the FAZ rifles are marked on the left receiver