Dungeons and Dragons 5E is largely designed as a class role oriented level based system.

The game makes large assumptions about the level of combat that will be going on, fantastical heroes overcoming odds, and all manner of magic.

Most post-apocolypse games tend to be light on combat, gritty, and non-magical.

So already we have some issues. Most post-apoc games focus on harsh wound penaties, D&D has abstracted hit points that are non-penalizing. D&D is very poor at handling social situations, and most post-apoc games tend to have social skills be pretty important.

I can keep going if you need more examples, but the core problem is we still need more information from the OP.

Magic? Psionics? RADIATION! (the pseudo-magic kind that makes Hulks)? Is it gritty? Is it combat focused? Will there be a lot of social situations? Who will the primary opponents be? D&D assumes a certain amount of big combats for XP (or yes otherwise "overcoming" the encounter).