The following item was made with a 5th level ranger in mind. The goal was to create an item that is mechanically fitting, and combat-relevant but not a weapon or armor.
Amulet of the Predator
Wondrous item, uncommon (requires attunement)
While wearing this amulet, you gain a +5 bonus to initiative rolls. Whenever you take the attack action on a first round of combat, you can make an additional attack with the same weapon.
Related discussions on magic items Weapon that allows an extra attack (as bonus action) every turn: Which rarity level is appropriate for this nerfed Scimitar of Speed with no bonus to attack and damage rolls?
Discussion of Sentinel Shield which gives improved initiative rolls: How powerful is a Sentinel Shield really?
As an alternative, I thought about adding proficiency instead of flat +5. There are features in the game that do similar things, although it seems, no official feature does exactly this. See the following question. Is There A Non-Homebrew Way To Add Proficiency to Initiative?
Question Is this item completely unbalanced or abusable? Is it wildly inappropriate for level 5 / as uncommon item? If either variant (+5/+proficiency) is a lot more powerful than the other one, I’d be interested in the reasoning as well.