5x3x3 Cube

Step 1

I start by just doing a layer solve with either the white, yellow, green or blue face as the first layer. Ignore the two 1x3x3 layers that pad a 3x3x3 as you restore both shape and color. The next step addresses the finaly layer of the well-known layer method.

Step 2

The final layer becomes interesting only because the corners don't necessarly solve, though the edges do. To remedy this case, you must realize that there is ambiguity in two of the four edges in the final layer. Two of those edges can be positioned on either side of the cube. The edges mentioned here are those that connect with the 1x3x3 extraneous layers. What you simply need to do is swap their positions, and then the corners will tri-cycle into place.

Step 3

With the inner 3x3x3 solved, you now need ony solve the two 1x3x3 layers. I solve edges, then corners in one layer, then the same in the other.

Adapted for this puzzle, a useful and well-known sequence for edge perumtation is A,B,Ai,Bi where A=2R,U,2Ri,Ui and B=2Li,Ui,2L,U.

Tri-cycling corners in the last layer may require a setup of 2F if you are using some varient of 2[U,2R,Ui,2R].