After building the 3x3 centers you can proceed with Pairing Edges like the 4x4x4 puzzle. The Last 2 Edges (L2E) can be solved with the algorithms below. Once completed, the cube can be solved like a regular 3x3x3 puzzle (Reduction).
L2CLast 2 Centers
The algorithms depicted in this section doesn't cover every scenario. I suggest using them as training wheels to help you understand the cube mechanics.
Here are the "Last 2 Edges" and parity cases you can encounter while solving the 5x5x5. Hold the cube so that the two edges to solve are at Front and Back of the Up layer.
