Found with PFGW Version 3.7.5

5582^7575-7575^5582 is 2-PRP! (31.5549s+0.0031s)
5582^7575-7575^5582 is 3-PRP! (25.9601s+0.0025s)
5582^7575-7575^5582 is 5-PRP! (24.1285s+0.0024s)
5582^7575-7575^5582 is 7-PRP! (25.7131s+0.0022s)
5582^7575-7575^5582 is 11-PRP! (23.9331s+0.0025s)

Primality testing 5582^7575-7575^5582 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.06% proof)
5582^7575-7575^5582 is Fermat and Lucas PRP! (166.7971s+0.0049s)

To be completed...