Full fathom five

I just ran across the phrase "full fathom five", meaning something like "completely sunk into despair". I like the sound of it.

I took a look in the archives here but all I could find were two discussions about "sea-change". Apparently the phrases "full fathom five" and "sea-change" were spoken by Ariel in The Tempest.

But does anyone know the origina of "full fathom five"? Is it from The Tempest originally?

This is Ariel's song from The Tempest:

Full fathom five thy father lies;
Of his bones are coral made;
Those are pearls that were his eyes:
Nothing of him that doth fade
But doth suffer a sea-change
Into something rich and strange.
Sea-nymphs hourly ring his knell

Whether it originated with Shakespeare I don't know, although it seems likely.

Thanks, but I was hoping that someone might know the significance of "five fathoms". For example most of us would grasp "six feet under" as a typical burial depth for a deceased person. Could this be a typical depth for someone sent to Davy Jones' Locker?