Caution! Partial Rant at manufacturers that report crazy specifications !
Ok... I've actually been wondering about this reporting of anything wider than 20-20,000 Hz. Whether it be for a power amp, a headphone amp, a DAP, A DAC, Speakers, or a Headphone/IEM/Earbud. And like the "HiRes" sticker means the device can send out frequencies up to something like 40,000 Hz. (Again inaudible for most humans)
1) When all we had were stereos, almost all of them had a low frequency filters to minimize/delete sound below 20hz. WHY? Well 2 reasons. First, Those frequencies take a lot more energy, watts, power to drive. AND with speakers, trying to make a woofer move at anything below 20hz, was asking to possible damage the Woofers. Second, I am not sure if anyone can reliably hear below 20Hz. Below 20 Hz is more likely to be felt as vibration, than actually heard from what I remember.
2) So Today we have "tiny speakers" (DD) and other kinds of drivers that were probably never intended to see frequencies below 20Hz, Why would I want to waste battery power to send under 20Hz sound to a device that would probably get damaged if driven to a level that one could actually fee or hear inside the ear? Let alone the damage those powerful, (silent to most all of us), under 20Hz frequencies would do to your ears/hearing. ( Recently saw IBASSO 160 spec saying 10hz - 40,000Hz. (remember the 10hz, not 100% sure of the 40K). Some suppliers don't even show lower frequency, even if their device could produce it, in their specifications. Flat output down to 20Hz if all you need in a DAP, and for a headphone to reproduce.
3) It is actually pretty difficult to reproduce under 20 Hz with Speakers. Even most Sub-Woofers people but don't really produce much sound below 20Hz. A few do, and they really can shake a house and take a lot of power to drive.
4) Specs that say 5Hz to 40KHz, really say almost nothing. I am sure that with sensitive enough equipment, and old transistor radio could be given that spec. Without a +/- 3dB, or +/- 10dB after the frequency range it could be +/- 30dB and so, some of that range would be produced at a very quiet/low volume.
5) I would doubt that you would find much recorded music that has any sound below 20 Hz. If there were any in the original performance, it's usually deleted/filtered out in the digital recording process.
You will never hear 5Hz, and the headphones will never produce that low a frequency at any detectable volume. IF, it could produce 5 to 20Hz sound, And there was significant sound in that range in the recording/file. you would probably be sending 20-30% of your power to the headphones to feel them shake on your ears.