On 4x4x4 I just remember the last letter of the last corner that's giving me parity. I then say that letter and the word parity, I use this so that it also goes into my auditory memory.
So if the last letter in my cycle is K I would say "K parity". Then, after solving centers, I setup piece K into the U layer and perform a PLL alg plus swapping the wings back.
On 5x5x5 I actually cycle the buffer to the last piece, and then to an already solved location on the U layer. This creates a double swap on the U layer. I do the same for midges. This creates a PLL case on the U layer, and I remember that PLL case by saying it out loud. So I might say "left N perm", "T perm", "upside down T-perm", "J perm", "R-perm" etc.
The reason I do the extra cycles on 5x5 is I have found that if I use the same approach as for 4x4x4 I often forget the parity pieces after solving both t-centers and x-centers. In order to alleviate this memory interference, I make the parity cycle easier to remember. I know it probably slows me down a bit for the two extra cycles, but I still solve fairly fast on 5BLD (dare I say it), and I feel that this method makes me more accurate and get fewer DNFs due to parity.