[muskatas]

I would agree with doctorabg you most likely have a problem on mechanical side. But it may help if you could tell us more about it. Why injectors were replaced? Are brand new ones put it? Does engine sound normal for those 5 seconds? Does it run at stable idle rpms and suddenly dies or does it struggle to reach idle level? Does it react to throttle for those 5 seconds?

Wild guess could be blocked air intake (what is MAF reading while it runs?), blocked exhaust (can you feel it?). You can also look at live data and look for any anomalies during those 5s. Check diesel amount flowing through injectors return line as well.

Give us something, we are not fortune tellers here

Injectors were replaced with used ones, corrections of "new" injectors was writen to DDE. Engine sounds normal and idle is normal for those 5 seconds, second start and engine works 3-2 seconds and third time only cranks. Tried disconect MAF - rough idle from beginning of start than. RPMS are idle for those 5 seconds with MAF. It runs in idle and than starts to die but not so suddenly (looks like someone turns of fuel supply). Engine reacts to throttle if it is kicked down before engine start (but only goes to ~3000rpm). If throttle is kicked down after engine is on - no reaction.
Today "new" injectors were replaced with old ones - same thing. Nothing more were changed, only injectors. Before this car was running fine (only a lot smoke on throttle and rough engine idle, diagnostics showed 3 almost dead injectors).
I would say it could be rail pressure sensor, but during those five seconds it is normal 300-350. Didnt checked MAF readings during those 5 seconds.