Final answer:
Damage to the hypoglossal nerve (CN XII) is most likely when a patient sticks out their tongue and it deviates to one side during an oral examination.
Step-by-step explanation:
When a patient sticks out their tongue and it deviates to one side, it suggests injury to the hypoglossal nerve (CN XII). The hypoglossal nerve controls the movement of the tongue, and if it is injured or damaged, it can cause the tongue to deviate. The other cranial nerves mentioned (CN V, CN X, and CN VII) are not directly involved in tongue movement, so they are less likely to be injured in this scenario.