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I am in the process of solving "every" 5x5x5 alg involving middle edges and wings edges and combinations of both wing and middle edges up to 12 moves in length. I have completed depth 11 and 1 of the 45 starting moves through depth 12.

The process started out very simply:

R2 3U R2 3U'

...and now gets a little more complex...

3F' R2 F' 3F 2U2 B U2 B' 2U2 F

...and includes stuff a human might never think about using in a million years...

R L 2U2 3U R' D2 R 2U2 3U' L' F2 R'

I'll be integrating them into my 5x5x5 solving program when the entire computation is done. The solver will be able to scan the list quickly, apply the algs, and determine which one nets the best progress towards solving the middle and wing edges simultaneously. This should produce very short, highly optimal solutions. Of course, I'll still need to add algs of length 13 and up to be able to handle any situation, but this can't be done with the current version unless I do it manually. So, if anyone wants to point me to a list of algs 13 moves and up that are necessary for the last layer cases involving parity, let me know.
 
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Not sure how easy this E-perm is to finger trick for somebody who's good, but it's easier for me than the x' R U' R' D R U R' D' R U R' D R U' R' D' that I learned first. It's really just a different angle of one that's already in the list. Swaps FR with FL and BR with BL, and the affected face ends on the front.

F' r U R' U' r' F l2 F L' F' l' U L U'
 
Not sure how easy this E-perm is to finger trick for somebody who's good, but it's easier for me than the x' R U' R' D R U R' D' R U R' D R U' R' D' that I learned first. It's really just a different angle of one that's already in the list. Swaps FR with FL and BR with BL, and the affected face ends on the front.

F' r U R' U' r' F l2 F L' F' l' U L U'
The last move should be a u'

Also, this alg is very awkward because of all the fat turns.
 
The last move should be a u'

Also, this alg is very awkward because of all the fat turns.

U' is correct, unless you prefer d'. Fair enough on the wide turns. They were an effort to eliminate B moves and cube rotations. It probably also depends some on the cube. Mine has a tendency to misalign layers and lock up using the RURD alg.
 
Not sure how easy this E-perm is to finger trick for somebody who's good, but it's easier for me than the x' R U' R' D R U R' D' R U R' D R U' R' D' that I learned first. It's really just a different angle of one that's already in the list. Swaps FR with FL and BR with BL, and the affected face ends on the front.

F' r U R' U' r' F l2 F L' F' l' U L U'

As I don't really enjoy the E perm, I found your alg quite interesting, but the main drawbacks for me are the "l" combined with Fs and F's, therefore I'd rather go instead with F' r U R' U' r' F l R U L' U' R' U L U'. The "l2" is transformed into "l R" and the rest of the sequence is only {R, U, L} based. The beginning is not practical for OH though.
That being said I didn't test the alg deeply enough to ensure that I'll use it in the future. Thanks anyway!
 
I didn't know where to stick this comment... and I am not really sure if it qualifies... but I stumbled upon a 10-move J-PERM.
But it isn't a J ... Perform a standard J-perm(b) on a solved cube followed by U', and that is the pattern this will resolve.

With the two "correctly positioned" cubies in UF and URF locations:
R L U2 R' U' R U2 L' U R'

I haven't seen it written down like this... so I decided to share. Let me know if I'm way off. Thanks :-)
 
I didn't know where to stick this comment... and I am not really sure if it qualifies... but I stumbled upon a 10-move J-PERM.
But it isn't a J ... Perform a standard J-perm(b) on a solved cube followed by U', and that is the pattern this will resolve.

With the two "correctly positioned" cubies in UF and URF locations:
R L U2 R' U' R U2 L' U R'

I haven't seen it written down like this... so I decided to share. Let me know if I'm way off. Thanks :)

Nice! There's this 10-mover as well: B2 L U L' B2 R D' R D R2. I believe that 10 is optimal and I haven't seen yours before!
 
I didn't know where to stick this comment... and I am not really sure if it qualifies... but I stumbled upon a 10-move J-PERM.
But it isn't a J ... Perform a standard J-perm(b) on a solved cube followed by U', and that is the pattern this will resolve.

With the two "correctly positioned" cubies in UF and URF locations:
R L U2 R' U' R U2 L' U R'

I haven't seen it written down like this... so I decided to share. Let me know if I'm way off. Thanks :)
This is the inverse of the mirror of the most popular Ja alg on algdb. It is move optimal and flows really nicely though.
 
I believe that I have found a new OLL alg. it solves the Chameleon case, where normally it would be solved as r U R' U' r' F R F', you would solve it as L' R' U R U' L U R' U' R'. I realize that this alg is 2 moves longer than the former, however I do think it is faster. hopefully you guys will agree with me.
 
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