I was told to 'Monitor the fuel pressure' when the car stars to miss and looses all power, the idel drops down, but after 5min driving goes back to normal then happens again ten min later

NO car or VIN told at all,just a year,
no maker, no model , no engine told and VIN covers that.
so now answers must be generic or dead wrong.
even mine, (grin!)
we have no petrol cars here ours are Gasoline so I know you are not USA easy.
the car needs service, for sure,
not told how well it drives, in all modes of use
idle, slow, , fast, uphills or WOT- wide open throttle)
not told scan the PCM and see DTC errors?
cutting out is 3 things.
1: spark loss or just misfiring,
2: or all engine power (HP)_ cuts off, like light switch.
3: the power goes off slow (HP) as does when fuel pressure drops. gentle loss

not told can fast right foot. save a stall. if does stall
is there exhaust parts with damage, leaks ,cracks or parts falling off??
Fluffing to me means exh, parts damaged. cracks.
or header flange loose or exh man cracked or loose.
looking there is what a tech does. fully and with due care not missing obvious damage.
O2 sensor fell off.?
get car serviced.

Monitor the fuel pressure when you are driving and see if it drops under a load.

Monitor the fuel pressure when this happens.

You probably have worn main bearings and worn cam bearings try a can or two of STP also would be nice to know what car and engine to better advise you .

Check oil level on dipstick. Check for loose connection on oil pressure sender unit. Have the oil pressure checked using a master gauge.

Sounds like the fuel pump pressure may be set too low. When you have the throttle open the TPS (throttle position sensor) sets the spark and fuel for a given demand.

When the demand is greater than the amount of pressure you have, the pressure drops and the engine is gas starved. The fuel pressure regulator is not responding fast enough but it is limited by the pressure your pump is making.

You need to get the fuel pressure checked. If the pressure is okay then the regulator is sluggish.

I would start by checking your ignition system, mainly the ignition coil. Sometimes when they get hot they fail and when they cool down they work properly. I would also check to see if the fuel pump may be overheating as well. Connect a fuel pressure guage to the system and watch the fuel pressure after you drive it. When it starts to act up if the fuel pressure goes wild you will have your answer.

replace your fuel filter best way to diagnose this one to start, find a way to monitor your fuel pressure if the filter had no effect, do you have any codes *** up ? and if so what are they, let me know, if not you might have a defective fuel pump, the pressure reading will tell, over 40 psi is good.

the throttle position sensor is gone, or the fuel pump, is not giving enough fuel, have the pressure read, and get back to me. im assuming it will be the sensor though.

The fuel presure should be at least 60- 66 psi key on engine off, and then drop some when started, if it doesn't go any higher than 50 psi that would explain your backfire concern. If it is low then the fuel pump is weak. I have also seen soot on the little wires inside the Mass Airflow Sensor cause a concern like this.