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EOL5E for a method I'm working on. It's in the New Method Idea Substep Etc. Thread.

Spoiler

U R' U' R' U' R' U R U R (10f*)
U2 R' U' R' U' R2 U R U R (10f*)
U' R' U' R' U' R U R U R (10f*)
R' U' R' U' R U R U R U' (10f*)
R' U' R' U' R2 U R U R U2 (10f*)
R' U' R' U' R' U R U R U (10f*)
U R' U' R' U' R U R U R U2 (11f)
U R' U' R' U' R2 U R U R U (11f)
U2 R' U' R' U' R U R U R U (11f)
U2 R' U' R' U' R' U R U R U' (11f)
U' R' U' R' U' R2 U R U R U' (11f)
U' R' U' R' U' R' U R U R U2 (11f)
R U R U R U R' U' R' U' R2 (11f)
R U2 R U R U R2 U' R' U' R2 (11f)
R U' R U R U R U' R' U' R2 (11f)
R2 U R U R U' R' U' R' U' R' (11f)
R2 U R U R2 U' R' U' R' U2 R' (11f)
R2 U R U R' U' R' U' R' U R' (11f)
R2 U2 R U R U R2 U' R' U' R (11f)
R2 U2 R U2 R2 U2 R2 U2 R U2 R2 (11f)
R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2 (11f)
R2 U' R U R U R U' R' U' R (11f)
R2 U' R' U R U R U R' U' R (11f)
R2 U' R' U' R U R U R U' R (11f)
R2 U' R' U' R2 U R U R U2 R (11f)
R' U R U R2 U' R' U' R' U2 R2 (11f)
R' U R U R' U' R' U' R' U R2 (11f)
R' U R U' R' U' R' U' R U R2 (11f)
R' U R' U' R' U' R' U R U R2 (11f)
R' U2 R U2 R2 U2 R2 U2 R U2 R (11f)
R' U2 R' U2 R2 U2 R2 U2 R' U2 R (11f)
R' U2 R' U' R' U' R2 U R U R2 (11f)
U R U R' U2 R U' R' U' R U2 R' (12f)
U R U' R2 U2 R2 U R' U' R' U2 R (12f)
U R2 U2 R2 U2 R2 U' R2 U2 R2 U2 R2 (12f)
U R2 U2 R2 U' R U R U2 R' U' R' (12f)
U2 R U' R' U' R U2 R' U R U R' (12f)
U2 R2 U R' U' R' U2 R U R U' R2 (12f)
U2 R2 U2 R2 U2 R2 U2 R2 U2 R2 U2 R2 (12f)
U' R U R U2 R' U' R' U R2 U2 R2 (12f)
U' R U2 R' U R U R' U2 R U' R' (12f)
U' R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2 (12f)
U' R' U2 R U R U' R2 U2 R2 U R' (12f)
R U R U2 R' U' R' U R2 U2 R2 U' (12f)
R U R' U2 R U' R' U' R U2 R' U (12f)
R U2 R' U R U R' U2 R U' R' U' (12f)
R U' R2 U2 R2 U R' U' R' U2 R U (12f)
R U' R' U' R U2 R' U R U R' U2 (12f)
R2 U R' U' R' U2 R U R U' R2 U2 (12f)
R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2 U' (12f)
R2 U2 R2 U2 R2 U2 R2 U2 R2 U2 R2 U2 (12f)
R2 U2 R2 U2 R2 U' R2 U2 R2 U2 R2 U (12f)
R2 U2 R2 U' R U R U2 R' U' R' U (12f)
R' U2 R U R U' R2 U2 R2 U R' U' (12f)
U R U R U R U R' U' R' U' R2 U' (13f)
U R U R U2 R' U' R' U R2 U2 R2 U2 (13f)
U R U2 R U R U R2 U' R' U' R2 U' (13f)
U R U2 R' U R U R' U2 R U' R' U2 (13f)
U R U' R U R U R U' R' U' R2 U' (13f)
U R U' R' U' R U2 R' U R U R' U (13f)
U R2 U R U R U' R' U' R' U' R' U' (13f)
U R2 U R U R2 U' R' U' R' U2 R' U' (13f)
U R2 U R U R' U' R' U' R' U R' U' (13f)
U R2 U R' U' R' U2 R U R U' R2 U (13f)
U R2 U2 R U R U R2 U' R' U' R U' (13f)
U R2 U2 R U2 R2 U2 R2 U2 R U2 R2 U' (13f)
U R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2 U2 (13f)
U R2 U2 R2 U2 R2 U2 R2 U2 R2 U2 R2 U (13f)
U R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2 U' (13f)
U R2 U' R U R U R U' R' U' R U' (13f)
U R2 U' R' U R U R U R' U' R U' (13f)
U R2 U' R' U' R U R U R U' R U' (13f)
U R2 U' R' U' R2 U R U R U2 R U' (13f)
U R' U R U R2 U' R' U' R' U2 R2 U' (13f)
U R' U R U R' U' R' U' R' U R2 U' (13f)
U R' U R U' R' U' R' U' R U R2 U' (13f)
U R' U R' U' R' U' R' U R U R2 U' (13f)
U R' U2 R U R U' R2 U2 R2 U R' U2 (13f)
U R' U2 R U2 R2 U2 R2 U2 R U2 R U' (13f)
U R' U2 R' U2 R2 U2 R2 U2 R' U2 R U' (13f)
U R' U2 R' U' R' U' R2 U R U R2 U' (13f)
U2 R U R U R U R' U' R' U' R2 U2 (13f)
U2 R U R U2 R' U' R' U R2 U2 R2 U (13f)
U2 R U R' U2 R U' R' U' R U2 R' U' (13f)
U2 R U2 R U R U R2 U' R' U' R2 U2 (13f)
U2 R U2 R' U R U R' U2 R U' R' U (13f)
U2 R U' R U R U R U' R' U' R2 U2 (13f)
U2 R U' R2 U2 R2 U R' U' R' U2 R U' (13f)
U2 R2 U R U R U' R' U' R' U' R' U2 (13f)
U2 R2 U R U R2 U' R' U' R' U2 R' U2 (13f)
U2 R2 U R U R' U' R' U' R' U R' U2 (13f)
U2 R2 U2 R U R U R2 U' R' U' R U2 (13f)
U2 R2 U2 R U2 R2 U2 R2 U2 R U2 R2 U2 (13f)
U2 R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2 U (13f)
U2 R2 U2 R2 U2 R2 U' R2 U2 R2 U2 R2 U' (13f)
U2 R2 U2 R2 U' R U R U2 R' U' R' U' (13f)
U2 R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2 U2 (13f)
U2 R2 U' R U R U R U' R' U' R U2 (13f)
U2 R2 U' R' U R U R U R' U' R U2 (13f)
U2 R2 U' R' U' R U R U R U' R U2 (13f)
U2 R2 U' R' U' R2 U R U R U2 R U2 (13f)
U2 R' U R U R2 U' R' U' R' U2 R2 U2 (13f)
U2 R' U R U R' U' R' U' R' U R2 U2 (13f)
U2 R' U R U' R' U' R' U' R U R2 U2 (13f)
U2 R' U R' U' R' U' R' U R U R2 U2 (13f)
U2 R' U2 R U R U' R2 U2 R2 U R' U (13f)
U2 R' U2 R U2 R2 U2 R2 U2 R U2 R U2 (13f)
U2 R' U2 R' U2 R2 U2 R2 U2 R' U2 R U2 (13f)
U2 R' U2 R' U' R' U' R2 U R U R2 U2 (13f)
U' R U R U R U R' U' R' U' R2 U (13f)
U' R U R' U2 R U' R' U' R U2 R' U2 (13f)
U' R U2 R U R U R2 U' R' U' R2 U (13f)
U' R U' R U R U R U' R' U' R2 U (13f)
U' R U' R2 U2 R2 U R' U' R' U2 R U2 (13f)
U' R U' R' U' R U2 R' U R U R' U' (13f)
U' R2 U R U R U' R' U' R' U' R' U (13f)
U' R2 U R U R2 U' R' U' R' U2 R' U (13f)
U' R2 U R U R' U' R' U' R' U R' U (13f)
U' R2 U R' U' R' U2 R U R U' R2 U' (13f)
U' R2 U2 R U R U R2 U' R' U' R U (13f)

I'm putting together a list of 5x5x5 algs that my program discovered. The ones shown in this post I haven't seen anywhere else. Right now, the program can perform brute force searches through 12 moves, but I'm working on improving this. If you would like it to see if one of your algs has a quicker solution, post it here and I'll give it to the program.

By fiddling around I found this pure 3-corner twist:
F2 R U R' U' R U R' U' F2 U' L' U' L U L' U' L U2
The change from right hand to left hand is a little awkward but apart from that I really like this alg. I still have to find out whether it is good though.

I figured out the bottom one as the second half of an E perm. It is one of the 15 or so COLLS I use and I agree that it flows quite well. I use a different alg for the first one though.