5e does not have a similar Corruption rule for the Nine Hells
Some of the planes have optional rules, as presented in the DMG.
The Nine Hells does have an optional rule, but it's not corruption, it's called "Pervasive Evil" and doesn't do the same thing as what you were looking for (DMG, p. 64):
Evil pervades the Nine Hells, and visitors to this plane feel its influence. At the end of each long rest taken on this plane, a visitor that isn't evil must make a DC 10 Wisdom saving throw. On a failed save, the creature's alignment changes to lawful evil. The change becomes permanent if the creature doesn't leave the plane within 1d4 days. Otherwise, the creature's alignment reverts to normal after one day spent on a plane other than the Nine Hells. Casting the dispel evil and good spell on the creature also restores its original alignment.
The Abyss has an optional rule called "Abyssal Corruption", which is on page 62 of the DMG, but
a) it isn't to do with the Nine Hells, and
b) it still isn't anything like the optional rule you were hoping to find.
If you are the DM, you could always come up with your own optional rules for any plane, but as it stands, RAW, the Nine Hells only has "Pervasive Evil".