I apologize if my posts concerning advertising irritate you. The problem is that there is no thread that is a good thread to get the issue addressed and it should be.

I think other videos will only confuse the issue further so I will stick to the videos you have posted. In the cold start video the left bank (the first bank) sounds normal to me. The right bank does not. By how sharp the noise becomes it sounds like it is coming from the middle of the right bank. Since I don't know what the temperature was or what oil you are using etc. I can't be sure it really is a problem and the second video with the engine up to operating temperature sounds normal.

I troubleshoot rather than speculate the core cause of an issue. My first check would be to see if/and how long it takes for the sound to go away from an idling cold start, no reving. The longer it takes the more likely a problem. In addition I would use an automotive stethoscope to pinpoint the loudest point to further narrow the cause possibilities. If you don't have one you can use a length of hose, anything with a hole through it, even a piece of metal that will carry the sound from the point of contact on the engine to your ear. Since sound travels so easily, once you have found where it seems the loudest and most crisp, move to all areas adjacent to that point to be sure you are at the right spot.

I think it would be very beneficial if you did another video. Start from a cold start--have someone else record the video so we can hear it just as it starts. Then record what it sounds like when the oil is at operating temperature. In both recordings do both sides of the of the engine and get close to the valve covers to eliminate as much wind noise as possible going front to back, back to front. Go very slow. In the cold start video it don't sound like you need to spend much time on the left bank since the noise seems far more prominent on the right.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas