Found with PFGW Version 3.6.0

5675^6002-6002^5675 is 2-PRP! (21.2359s+0.0040s)
5675^6002-6002^5675 is 3-PRP! (22.1189s+0.0028s)
5675^6002-6002^5675 is 5-PRP! (22.0190s+0.0041s)
5675^6002-6002^5675 is 7-PRP! (22.0167s+0.0027s)
5675^6002-6002^5675 is 11-PRP! (22.0150s+0.0042s)

Primality testing 5675^6002-6002^5675 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.22% proof)
5675^6002-6002^5675 is Fermat and Lucas PRP! (106.8833s+0.0029s)

To be completed...