Found with PFGW Version 3.8.0

5059^11282-11282^5059 is 2-PRP! (35.4530s+0.0039s)
5059^11282-11282^5059 is 3-PRP! (35.4879s+0.0042s)
5059^11282-11282^5059 is 5-PRP! (35.3386s+0.0039s)
5059^11282-11282^5059 is 7-PRP! (35.6629s+0.0038s)
5059^11282-11282^5059 is 11-PRP! (35.4875s+0.0045s)

Primality testing 5059^11282-11282^5059 [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 0.03% and helper 0.01% (0.10% proof)
5059^11282-11282^5059 is Fermat and Lucas PRP! (173.6987s+0.0124s)

To be completed...