Found with PFGW Version 3.7.5

387^5282-5282^387 is 2-PRP! (7.2237s+0.0018s)
387^5282-5282^387 is 3-PRP! (6.6995s+0.0016s)
387^5282-5282^387 is 5-PRP! (7.0392s+0.0023s)
387^5282-5282^387 is 7-PRP! (7.6073s+0.0018s)
387^5282-5282^387 is 11-PRP! (8.0700s+0.0019s)

Primality testing 387^5282-5282^387 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N+1 BLS with factored part 0.13% and helper 0.07% (0.46% proof)
387^5282-5282^387 is Fermat and Lucas PRP! (38.3219s+0.0041s)

To be completed...