The method suggested to carry out the “Professor” (5x5x5) is the
following one: to carry out the edges of the 5 layers then centers.
Let us start with the second layer:
For that, we will carry out the first layer. This stage being very easy
to make, we will not develop in detail the realization of the first layer.
As for the 3x3x3, it is necessary that the first layer is aligned with the central cubes (blue edges of with dimensions of the blue central cube).
When you finish positioning the edges of the second layer,
your cube will resemble that: |

|
To place the edges of the second layer, two formulas!!! and know them
already to you!: in fact the formulas make it possible to place the
edges of the second layer of the 3x3x3.
2 cases are thus possible:
1 - The edge of bottom (on the fifth layer) must come to replace the edge of right-hand side (second layer):

|
Apply the following formula:
D' R' D R D F D' F'
|

|
2- The edge of bottom (on the fifth layer) must come to replace the edge of left (second layer):

|
Apply the following formula:
D L D' L' D' F' D F
|

|
Particular cases:
It is possible that an edge soint placed well but badly directed.
In this case, use the fortmule “to release” the edge badly directed (green/orange in this example) towards the fifth layer.
It is then enough to place correctly the edge orange green/with formula
1 or 2 according to whether it is on the right or on the left.
|

|
Another particular case, it is possible that an edge is placed on the fourth layer (and not on the fifth).
In this case, use the formula which makes it possible to descend the
edges from the fourth layer on the fifth (it later will be re-examined).
In this example use the fortmule L
D' L' d' L D L' d
|

|
In the opposite case, use the following formula:
R' D R d R' D' R d'
|
 |
When the 4 edges of the second layer are correctly placed, your cube must resemble that:

Let us pass now to the edges of the third layer.
|