This item can be found rarely inside the [Tiny Titanium Lockbox], itself found extremely rarely inside the [Bag of Fishing Treasures] rewarded from completing Marcia Chase's daily fishing quests in Dalaran.
This ring is a continuation of the numerical fishing ring joke that includes [The 1 Ring] and [The 2 Ring]. The flavor text is in reference to the non-existence of the 3 or 4 Rings.
Wowhead has the drop rate of the The 5 Ring at 5% from [Tiny Titanium Lockbox], and the box itself at 0.2% from the [Bag of Fishing Treasures]. This suggests you have a 0.01% chance of getting The 5 Ring on any particular day, and an expected average of 10,000 daily fishing quests completed (over 27 years).
Direct reference and humorous variations on The One Ring, the most powerful item in Middle-Earth, which drives the plot of Lord of the Rings.