A genuine Jungle Carbine?

Welcome to the site! That rear sight is stamped steel and the first I have ever seen like that! I own 2 No.5/MK1's with the milled steel rear sights. (CORRECTION: This sight in his photo is a milled rear sight. I don't know why I thought it was the stamped steel rear sight but I stand corrected.).

With the star over the chamber & transverse screw through the forearm, it’s been to India.  It looks refinished and I can’t say if that was done in India, though they certainly scrubbed, remarked, and refurbished (and not necessarily all of those things, or in that order) plenty of these.

I have seen a Indian reworked No4.

It was completely remarked and had the screw through the forearm.

Thanks a lot for your comments.
Yes, the rifle has been refinshed, that much is clear. However, I don't know by whom or when.
Since all the known features of the genuine No. 5 are present, including the “lightening” on the barrel and under the trigger (deep inside the receiver), it is unlikely to be a fake. But it's not just the absence of any model markings that gives me pause, but also the serial number on the left side of the receiver, next to the stock. It is four digits long and begins with “K.” Charles R. Stratton writes in his book about the No. 4 and No. 5 (British Enfield Rifles Vol. 2) on p. 171 in Table F-14 that only ROF Fazakerley used single letters. On p. 169 in Table F-7 (ROZ Fazakerley No. 5), however, the letter “K” is not listed. But on p. 166 in Table F-1 (BSA No. 4), the letter “K” is listed among the No. 4 rifles from BSA for 1944. Very, very strange:
All hardware features prove that it is a genuine No. 5, but the serial number proves that it is a No. 4.

Translated with DeepL.com (free version)

A complete listing of ROF Fazakerley serial numbers is located on page 216 in my new book, A Collector's View:  The Lee-Enfield RIfle No. 4 and No. 5, Part 1 1931-1945, along with a detailed view on all the different rear sights that were factory and later armorer installed.