Found with PFGW Version 3.7.5

789^5992-5992^789 is 2-PRP! (10.5262s+0.0021s)
789^5992-5992^789 is 3-PRP! (10.4421s+0.0021s)
789^5992-5992^789 is 5-PRP! (11.5511s+0.0021s)
789^5992-5992^789 is 7-PRP! (12.9532s+0.0025s)
789^5992-5992^789 is 11-PRP! (12.5075s+0.0022s)

Primality testing 789^5992-5992^789 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.18% proof)
789^5992-5992^789 is Fermat and Lucas PRP! (68.5066s+0.0038s)

To be completed...