There is actually no difference between solving the 5x5x5 as with a 3x3x3 once you have solved the centers and the edges.
Simply treat the inner slices as a single slice and do everything the same as you would with the 3x3x3. Check out the
image below to see what I mean.
I will follow the same processes I used in the 3x3x3 section and the exact same algorithms as in the 4x4x4 section.
Note that I am not showing the algorithms used in the examples, they wouldn't be useful for you to use unless your cube happened to
be aligned exactly as mine.
First, let's move the top edges into place, then the top corners. 
Now let's solve the second layer. 


Now I flip the cube over to put the bottom corners into place and shift the last edges around. 
We've ended up in the fish pattern, so we apply the algorithm to solve the cube. 


Well, that's it, you now have a fully solved cube, congratulations!. Now why don't you try moving up to the 6x6x6.
