Lining up the edges on a 5x5x5 is pretty similar to the 4x4x4. I use 2 of the same methods. The only difference is having
3 pieces instead of two. To start off I'll 'cut across the centers' to line up pieces. Once I get down to just a few left
I switch to the 'opposing edges' algorithm.|
I think it is best to try and line up all 3 edge pieces together, although you could just pair up the outer two first and then move the middle edge in later. I started out following the latter method but found that it takes quite a bit longer than just lining up all 3 to begin with. In the examples below I'll show first how to cut across the centers and then how to use the algorithm. Your cube shouldn't look anything like these examples since none of your edges and corners will be in place yet. I am starting with a somewhat solved cube just to make it easier for you to see the impact of the moves.
In the first example I matched up the red/blue edges. Note that I had 4 edges messed up, 3 that each contained one of my red/blue pieces and a 4th in the Up/Right position. Just like in the 4x4x4 method you must have an edge to sacrifice after you move off your newly matched edge to a safe place.
In the second example I put the red/green outer edges opposite each other as well as the red/blue edges. You can see that none of the edges were destroyed but the algorithm is only useful for pairing the outer edge pieces. Sometimes the middle piece will be rotated improperly as seen in the red/blue edge. This is what is known as a parity issue. There are several potential parities and the people at www.bigcubes.com have a pretty comprehensive guide covering them. I am only going to show the 2 most common that I run into. If you find yourself with a different parity issue you should click on the link to visit their site and find a solution.
The two issues I see the most are the 'single edge flip' and the 'double wing swap'. Technically the wing swap is not a parity issue but I'll cover it below.
Now that your edges are lined up you can proceed to the Final Solve.