L5EOP, last five edges orientation and placement of the last first layer edge, is an experimental method for the 3x3x3 cube that is an alternative to L5E. In L5E the last five edges are first oriented without minding the permutation for the last first layer edge (normally the FD edge), then all five are permuted together. That makes 5 algs for L5EO (orientation) and 16 for L5EP (permutation). This method requires 20 algorithms for orientation and FD placement and on top of that you also need the 4 EPLLs that are used to end the solve.
In the cases where the last FL edge is solved by chance before this step (1:10) knowing ELL will help a good bit, aspecially for the 4flip case.
  Why L5EOP? Can't I do the same using L5E?
  Well, L5E is more elegant than this but here we are talking brute force, you will always have EPLL in the end and you know it, wich makes recog almost instant. And besides that, here you get a skip in 12 for the last step, without any force used L5E permutation skips in 1 of 60.
  If I use both then? some cases are only three turns to orient if you don't put the last FL edge.
  Yes, and ELL!
See also
Usage of the method
Roux Method; after F2B and CMLL you solve centres and the BD edge and you are here.
Columns First Methods; nearly the same as for Roux but there are two more edges to place (RD/LD) together with the centres after the columns are compleated.
Petrus Method; Build the 2x2x3 block and then you initially skip the "bad edges" step and just do the "finish F2L" part. Because edges are not oriented at this point the pairs will be diffrent, but still easy, (you can benefit from using the empty side). Then, if you do COLL you can use L5EOP after the pairs but better is to use CLL (or even CMLLs like R' U2 R U2 R U2 R U2 R') and do the edges after, it saves turns on average, end in EPLL. For OLL; edges after the pairs, OCLL and last PLL.
LBL, 3 piece cross, F2L as normally, L5EOP, COLL + EPLL or even ZBLL (it becomes an alternative to VHF2L) or for "Fridrich" the same start but any OLL that twist the corners before L5EOP (you can use shorter OLLs if you ignore edges) and last PLL (more or less a 2look OLL, not an option really, but you can benefit from having a empty side while building the pairs).
Cases
Testing a new image style:
This is the goal position for the five edges involved, UR, UF, UL, UB and FD. The four in U we only orient but the last one (yellow/green) must also be placed. If these images are not perfectly clear to you, then just click one of the algs in the listing for the particular case and you will have a virtual cube showing the case and another click on the play button and it will animate the turns for you.
If you got the last case, the one with all edges correctly oriented, and if the last D edge is still up, you can easily put it by doing AUF and then M' U2 M. Another option is to solve all the rest in one look using the permutations of L5E. The orientation skips 1:16 times. A compleate skip of this step (skip to EPLL) occures 1:80 times (total skip 1:960).
Note that all of these algorithms are written in the Western notation, where a lowercase letter means a doublelayer turn and rotations are denoted by x, y, and z. (how to add algorithms)
Click on an algorithm (not the camera icon) to watch an animation of it.

1+1 edge unoriented (1:4)
2+0 adjacent edges unoriented (1:4)
A20D

Use ELL to solve in one look.



2+0 opposite edges unoriented (1:8)
O20D

Use ELL to solve in one look.



3+1 edges unoriented (1:4)
4+0 edges unoriented (1:16)
40R/40L/40F/40B

40D

Use ELL to solve in one look.

