Yau5 method
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Yau5, not to be confused with Yau4, is a 5x5x5 speedsolving method proposed by Robert Yau. It can also be, and frequently is, applied to bigger cubes.
Yau5 is not the same as Yau (Yau4). While both have a partial cross step, Yau5 pairs edges differently from Yau4. See Steps below.
Steps
 Solve two opposite centers
 Solve 3 of the cross edges
 Solve the last 4 centers by solving the layer closest to the partial cross, then the next closest, etc.
 Solve the final cross edge
 Pair 4 2nd layer edges
 Solve 2 adjacent F2L pairs
 Pair the last 4 edges (+ parity on oddordered cubes)
 Solve like a 3x3x3 (+ parity on evenordered cubes)
Pros
 Cross and 2 F2L pairs are already done when you start the 3x3 step
 Easy edgepairing
Cons
 Centers are a little harder
 Difficult to find the right edges to pair