I was just taking a break from solving my 5x5x5 cube when I decided to check what kind of documentation it had here on e2. That said, here's a general outline as to how I like to solve him...

1. Solve the center nine tiles on each face by starting with one, then doing its opposite, then another and its opposite, then another and its opposite.
2. Solve four edge triplets and "store" them on the top layer.
3. Solve four more edge triplets and "store" them on the bottom layer.
4. Move one solved edge triplet down into the middle layer, twist the middle layer to solve a different edge triplet, store that one in the top layer, then untwist so that the first triplet is re-solved (and the centers are back to normal, also).
5. Finally, gather the three remaining unsolved edge triplets onto the front face.
6. Pray.
7. Screw around with these three for five or ten minutes until Wyrd smiles upon me and all triplets and all centers are solved.
8. Solve it as if it were a 3x3x3 cube which means...
9. Solving the entire white face (I always start with white since it is the easiest to find on a scrambled cube) except for one corner
10. Use that corner as a "key" to quickly place the middle layer edges
11. Place the final corner with the three-corner-swap algorithm
12. Fix the top layer with edge-switches and edge-switches-with-flip
13. Place the four top layer corners with the three-corner-swap
14. Finally, orient the top layer corners with the two-corner-twist, which rotates one corner upon itself clockwise and another corner upon itself counterclockwise.

Whew! Anyhoo, the whole process takes about twenty to thirty minutes but is very, very satisfying.

Furthermore, the 5x5x5 cube is, in my opinion, easier than the 4x4x4 cube. I believe that for some reason, even-sized cubes are less... stable than odd-sized cubes. For example, it's possible with the 4x4x4 to end up with the entire cube solved except for one edge pair, which is flipped upon itself. On the 3x3x3, this is impossible without taking the cube apart and re-assembling it incorrectly. Even on the 5x5x5, this situation is impossible; once you have all the edge triplets solved and all the faces fixed, there is a 0% chance of bizarre parity errors.

Now, to wrap up, the 5x5x5 is incredibly nifty for patterns. Anything you can do to a 3x3x3 can be done to a 5x5x5, EXCEPT there are two ways to treat the cube. For example, say you apply the algorithm U2 D2 L2 R2 F2 B2 to a solved 3x3x3. You'd get a lovely checkerboard. You can do the same with the 5x5x5 in two ways.

Consider this face:

CEEEC
EMMME
EMMME
EMMME
CEEEC

Where C is a corner piece, E is an edge, and M is the middle. You'd end up with a checkerboard with very fat center pieces. But consider this...

CCECC
CCECC
EEMEE
CCECC
CCECC

If you apply that algorithm you get a checkerboard with very fat corner pieces!! This pattern continues with all odd cubes, though anything larger than a 5x5x5 only exists as computer simulations.

Erm, yes. Anyway, 5x5x5 cubes are terrificly awesome and can be purchased from www.mefferts.com in two coloring schemes for about \$26. Yes, it's a little expensive, but shipping from China is included.