Found with PFGW Version 3.7.5

5304^7577-7577^5304 is 2-PRP! (32.3813s+0.0042s)
5304^7577-7577^5304 is 3-PRP! (27.8624s+0.0028s)
5304^7577-7577^5304 is 5-PRP! (23.9592s+0.0024s)
5304^7577-7577^5304 is 7-PRP! (27.5253s+0.0023s)
5304^7577-7577^5304 is 11-PRP! (25.4939s+0.0023s)

Primality testing 5304^7577-7577^5304 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.08% proof)
5304^7577-7577^5304 is Fermat and Lucas PRP! (167.3762s+0.0049s)

To be completed...