Probably real, most airsoft MP-5's don't have a burst function.
The short sight radius makes me think it was modified from an mp5k (real or airsoft). Whether it is real or not... I have no idea.
B&T stock?
I think its fake cause look at the mag release its twisted. Notice how its flat in the picture above. While real ones at profiled. See below
http://www.hkpro.com/mp5sdclose.jpg
Could be something along the lines of a HK94 or similar clone that's been shortened down somewhat and with a fake suppressor shroud covering the longer barrel.
It looks to long to be an MP5K and the bolt in the lower reciever aswell as the paddle release isn't right.
Just having burst/FA markings on the lower doesn't mean that there's a corresponding trigger group inside it
There is no airsoft MP5 with 4 positions (no TM, CA or Systema)...
A fake position on a TM MP5 J (Airsoft):
The stock is specially for use with helmets with a large front visor. Otherswise teh visor obstructs aiming...look at old SAS pictures...
(also not found as a replica airsoft thing)
something like this:
regarding the Mp5 body...ther are 2 types: polymer ( flat) and metal , with stamped surfaces...so I think real , maybe a 1 time custom order at H&K, happened before.
Ive seen that stock on mp5s before in mp.net, as for the rest I dont know.
as i wrote (twice), this is a mini uzi stock - this stock was designed long before visor helmets were used, and anyway israeli SF don't use visor helmets.
photos courtesy Isayeret
It is definitley MP5K length
edit- found it here http://www.rdts.com/MP5KSD.html