This video shows an explanation for an Advanced Edge Pairing method for the 5x5x5 Cube. The method used is as follows. First, you should match up edges on the middle layers (in the build ring) to form complete "tredges," or triple edge pieces. Then replace and store these tredges on the Up and Down faces of the cube. This method CAN be applied to any size big cube!
Once you have completely matched 8 tredge pieces and stored them on the Up and Down faces, you can then go on to solve the remaining 4 mixed up tredges left on the middle layers.