You can solve the 5x5x5 by reduction. That is, doing a few *new* steps and then solving it like a 3x3x3.
So here's the steps:
- Solve the Centers (3x3 grid on each face)
- Pair the Edges
- Solve like a 3x3x3
- Fix ParitySolve the Centers
If you can't figure out how to do this I suggest trying the following:
- Solve a 3x3 square on the White face
- Then solve a 3x3 square on the Yellow face
By now you should see that your movements are becoming more and more restricted. You'll end up mucking up the previous 3x3 square (or center) if you don't account for it. It should become intuitive, so practice solving these 3x3 centers individually until you can solve them all.Pair the Edges
Solving a 5x5x5 is like solving a 4x4x4 but with and extra Edge Pairing step involved. With a 4x4x4 you only need to pair up two edge pieces but the 5x5x5 needs three
edges to be paired up.
To keep things simple you can just pair up two edges at a time on the 5x5x5 and you'll end up with a bunch of edges that are paired plus one. You can then pair these odd edges up with the already paired edges and you'll have a group of 3.
Here's an algorithm you can use to create three groups of pairs: AlgSolve like a 3x3x3
I'm assuming you can solve a 3x3x3 so when you get to this stage you just need to solve it as such. When you're trying to Orient the Edges you might find that there's one group of edges where the two outside edge pieces have been flipped. This is a parity issue which you can ignore until the end of the solve if you so wish.Parity
This can happen on a 5x5x5: the alg
The same thing occurs on a 4x4x4: the alg
...another 4x4x4 parity issue here
There's heaps of web pages and videos that can better explain it. I hope this points you in the right direction :-)
Google is your friend :-P