What does Miraculous Fleece do?

The 5% is the tier 2 figure, and it applies to healing your Aniimo does, so it only earns its slot on a healer. On a damage dealer it does nothing useful.

That slot matters because an Aniimo carries a single held item and nothing else. Putting the Fleece on means giving up something like Ferocious Fang, the legendary general-purpose item that raises attack damage. For a healer that trade is easy. For a hybrid that heals a little and hits a lot, the Fang is usually the better use of the one item it gets.

The Fleece also appears with a 12% bonus to healing power, which is a larger figure than the 5% listed tier. Check the number on your own copy rather than assuming one or the other.

Not settled: Two figures exist for this item: 5% to healing done at its listed tier 2 and 12% to healing power. It is not settled whether these are different tiers or different stats. In the closed beta, tiered effects were unlocked by socketing runes, and that system was removed at launch, so beta-era tier figures may not match what the item shows now.