Wait, define what you mean by a parity error.
If you mean that the whole cube is solved but the side edges are flipped on one edge of the cube, then here's an algorithm to take care of that.
Note, when i say R or L, grip the two side layers on that side.
When i say 2 in front of the letter, turn it twice.
When there is an i after the letter, turn the layer counterclockwise.
The algorithm is:
2R 2B 2U L 2U Ri 2U R 2U 2F R 2F Li 2B 2R
Yes, it is 15 moves long.
The algorithm will flip the side edges on an edge of the cube. It will mess up the cube, but the centers are still solved and the edges are still together, so you can just solve the rest of the cube like a 3x3.
Think of doing so this way: the 3 edges that are together on the 5x5 is like the 1 edge on the 3x3, and the centers are like the centers of the 3x3. And the corners are just corners.