Found with PFGW Version 3.7.5

5998^7125-7125^5998 is 2-PRP! (48.9364s+0.0032s)
5998^7125-7125^5998 is 3-PRP! (47.0833s+0.0042s)
5998^7125-7125^5998 is 5-PRP! (50.1489s+0.0034s)
5998^7125-7125^5998 is 7-PRP! (47.8767s+0.0021s)
5998^7125-7125^5998 is 11-PRP! (46.0112s+0.0022s)

Primality testing 5998^7125-7125^5998 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
5998^7125-7125^5998 is Fermat and Lucas PRP! (224.4636s+0.0055s)

To be completed...