this BBEG is designed for 13th level PCs so the DCs in his fortress are X. They remain X even if the party comes ta him at 8th or 20th level.
The DC isn't a property of the fiction. It's a mechanical conceit. It can be set in various ways for various purposes. I assume that @Corrosive either (i) wants to set "fair" DCs, or (ii) wants to know what range of DCs will (roughly, on average) have what sorts of pacing consequences. Either of those seem to me like sensible things to think about when setting DCs.If a lower character attempts the same task, it will remain the same DC. When the character come back 5 levels later, it will still be the same DC, except that what was hard for them back then might be easy now.
DCs can also be used to establish the "feel" or details of the fiction. This will then put the burden of ensuring fairness and/or adequate pacing somewhere else. I don't know the full range of techniques D&D GMs use for this purpose. I suspect that player-side interventions - in particular, circumventing or significantly modifying DCs by the use of spells and other magic - play a fairly big role in this respect.
As for the "5 levels later": I don't know how often D&D play involves the same fictional situation, with no changes, at 5-level intervals. But I don't think it's that common, and so could probably be handled on an ad hoc basis if it were to come up.