Found with PFGW Version 3.7.5

5975^8526-8526^5975 is 2-PRP! (18.0827s+0.0015s)
5975^8526-8526^5975 is 3-PRP! (18.0178s+0.0016s)
5975^8526-8526^5975 is 5-PRP! (18.0818s+0.0016s)
5975^8526-8526^5975 is 7-PRP! (17.9834s+0.0015s)
5975^8526-8526^5975 is 11-PRP! (18.6233s+0.0016s)

Primality testing 5975^8526-8526^5975 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N-1 test using base 23
Running N-1 test using base 37
Running N+1 test using discriminant 43, base 2+sqrt(43)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
5975^8526-8526^5975 is Fermat and Lucas PRP! (158.3728s+0.0024s)

To be completed...