If you choose to "apply 5 damage to an ally", who gets the damage if your ally can only take 3 damage?

The option is satisfied or do you take the 2 damage difference on your investigator?

It all just goes on the one ally.

Rules Reference p7.

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An asset cannot be assigned damage beyond the amount of damage it would take to defeat the card, and cannot be assigned horror beyond the amount of horror it would take to defeat the card.

That only applies when you, the player, take damage and have to assign it among multiple cards. Snakebite explicitly damaged the asset itself, so you can (and, indeed, must) put all the damage on that card.

2 hours ago, rsdockery said:

That only applies when you, the player, take damage and have to assign it among multiple cards. Snakebite explicitly damaged the asset itself, so you can (and, indeed, must) put all the damage on that card.

Precisely.

The excerpt from the rules as quoted by @psmythirl doesn't include a crucial element, namely this:

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When an investigator or enemy is dealt damage and/or horror, follow these steps, in order:

[...]

The rules for damage assignment apply for the normal process of an investigator taking damage (if you are attacked by an enemy, say, or are hit by Grasping Hands). Snake Bite specifies:

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Deal 5 damage to an Ally asset you control.

This bypasses the normal rules for damage assignment (due to the Golden Rules). So the "Assign damage and horror" step is not used at all. Instead, you simply assign 5 damage to the chosen ally and any damage in excess of its health is ignored.

The wording for an otherwise identical effect that would overflow to your investigator would be something like "If you have an ally asset in play with at least 1 health: Take 5 damage. This damage must be assigned to an ally asset first."

Yeah, not many allies have more than 5 health. So mostly it's "poison one ally to its defeat." Unless that's a scary tough ally, maybe Trusted, or even twice-Trusted.

To be specific, Snake Bite will instantly defeat any Ally except a doubly-Trusted RGM or Agency Backup.