Which personality increases crit rate?

Personality is rolled at random on every Aniimo, wild spawns included, so the 5% is luck. It sits alongside the creature's randomly generated stat values, and the personality you get also shapes its combat behaviour and hands out its own stat bonuses. A crit rate bonus is one of those possible bonuses, not something every Aniimo has.

To see what you rolled, open the Aniimo tab. The personality appears as four letters at the top of the creature's page, an MBTI style code such as ENTP. If the roll is wrong for the job, Psyche Fruits reroll an Aniimo's personality traits. The reroll is random, so a fruit gives you another chance at the crit personality rather than a guarantee of it.

Do not confuse the crit bonus with the S trait. The S personality trait gives bonuses to damage, which is a different stat from crit chance.

What chasing crit costs you at home

Personality also decides how efficiently an Aniimo works homestead jobs such as crafting and gathering, and some personality perks give a 20% work efficiency boost at specific tasks like mining or particular crafting stations. Rerolling a good worker to fish for 5% crit chance can cost you that boost, so decide whether the creature is for fighting or for the homestead before you spend fruit on it.

Not settled: Which four-letter personality carries the 5% crit bonus is not established here, so check before rerolling and do not assume it is the S trait, which is tied to damage.