Tell us about yourself!
The algorithm for OLL parity (up-front edge flip) is r U2 r F2 r F2 r' F2 l F2 r' F2 r F2 r' F2 r' F2 l' r U2.After applying r2 U2 r2 U2 u2 r2 u2 PLL parity (2 corners swapped) becomes solvable.As for the edge pairing parity, you should treat the l' U L' U' l algorithm as a 3-cycle: http://puzzlesolver.com/data/30/images/step2move....If 4 edges remain, you should not let 2 edges to be solved at once.The last 3 edges to be paired should be set up so that the cycle solves them.This will avoid the edge pairing parity.
In fact, after l' U L' U' l, you can then do U L U' to see only the 3-cycle itself without anything else scrambled.
it's layer by layer
And also a modified version of this for 7x7!
I realized I can actually solve that by 4x4 edge pairing, reducing it to 5x5 centers! Yay!
Help, I have a parity case for centers on a 6x6.
it's spelled P, A, R, I, T, Y
I think in 5x5 you don't have to deal with parity (in the method I use), but in other hand there are more centers and edges to pair.
it's spelled p a r i t y
I use a somewhat different method: in both 4x4 and 5x5, I use l' U L' U' l to shift edges, and carefully plan the last 3 so that it perfectly reduces to 3x3. In case of 4x4, I also use OLL and PLL parity algorithms.