Another update and happy ending. Temps below in format Core Temp/ASUS Probe.
I have re-applied AS5 third time. Turned on system...
Idle temp: 39c/43c
2xPrime95: 63c/68c after ~ 5 minutes.
At that point I was quite disappointed with results.
Then I tried check the plastic fasteners. Tried pushed a little harder without pulling processor out. Pressed hard on on one, then another, and then I pressed quite hard on pin closest to CPU FAN mb contact... And I heard quite load crack sound... I thought sh%t, I broke my motherboard....
Immedeately turned on system, to check if it boots... And it did boot!
And what I see now?
Idle: 33c/37c
2xPrime95 after ~15 min: 48c/51c!!!
So, i guess that crack sound was final snap of the pin.. It was pretty loud to me...
Good part is that processor gets proper cooling now. I am quite happy about that.
Thank you very much everyone for advices and recommendations!!!!