iPhone 5 sounds awful while using headphone

[Perene]

And the other devices I tested here, including the iPhone 4 and a LG device, don't have this problem. I am using a Sony headphone (don't know the exact model). When I plug the headphone into this iPhone 5 (ND293BZ/A model) and visit any Youtube video (regardless of the app used) the sound is clearly INFERIOR to what I am getting with the others. I don't know how to describe the difference, but it sounds like I am listening to this:
https://en.wikipedia.org/wiki/LP_record

Instead of a clear sound. I tried using the same headphone in all these devices, and the difference was quite noticeable. This iPhone 5 uses iOS 10.3.3.

Any ideas how to fix this issue? Or this can't be fixed at all?

P.S. this is how the headphone looks like:
https://goo.gl/WGywWc

 

[BrianBaughn]

If the comparison results are close to the same with other headphones I'd say there's something wrong with the iPhone 5. If it's only with the Sony headphones I'd say there's something wrong with the connection between the iPhone 5 and the headphones.

Is it possibly the sort of "phasing" issue that one can get when stereo headphones aren't properly seated into the jack?