If I give something 5 damage with something with 9 Might, does it do 4 Might damage or 9?

It does 9 might damage.

In Riftbound, damage and Might are two completely separate mechanics. Damage marked on a unit does not reduce its Might, and a unit’s combat damage output is always equal to its current Might value, regardless of how much damage it has accumulated.

According to RiftJudge FAQ #2551:

"Does damage dealt to a unit reduce its might for combat damage purposes? Ruling: Damage does not reduce might. A unit deals combat damage equal to its printed might value regardless of how much damage it has accumulated."

For example, if your unit has 9 Might and has 5 damage marked on it, it is still a 9 Might unit and will contribute 9 damage during combat.