How about with an item like a belt of giant strength; after 24 hours the enhancement bonus is treated like an inherent bonus - how does that interact? Or if I took a class that gave an inherent bonus to something?
EDIT: And looking at the wish spell, it looks like inherent bonuses are capped at +5 but the item/class abilities go up to +6....
The belt of giant strength is treated as a PERMANENT bonus after 24 hours. That's not the same as saying it's now an inherent bonus. The belt is still an enhancement bonus. Becoming permanent has certain benefits listed in the entry. It will stack just fine with an inherent bonus to strength as it's granting an enhancement bonus.
The Belt of Giant Strength gives an Enhancement bonus, actually. The thing about wearing it for 24 hours means that, after 24 hours of wearing it, your strength is considered to permanently be the increased score for the purposes of prerequisites.
You actually can get inherent bonuses higher than +5, but I only know of two ways to do that and both of them require getting the Sorceror's bloodlines.
The others said the important things so:
We use a house rule that inheritance bonusses do indeed stack to a max of the normal 5 (unless otherwise higher limited).
This means that you CAN buy a manual or a tome +1 when you CAN afford it, and an adventure or 2 later, buy a new one, and actually use em.
Our reasoning is that you cannot sell the first manual/tome you read after you bought and read a new one...