Found with PFGW Version 3.7.5

5627^10304-10304^5627 is 2-PRP! (26.5647s+0.0016s)
5627^10304-10304^5627 is 3-PRP! (26.6137s+0.0015s)
5627^10304-10304^5627 is 5-PRP! (26.5887s+0.0015s)
5627^10304-10304^5627 is 7-PRP! (27.0506s+0.0018s)
5627^10304-10304^5627 is 11-PRP! (26.4799s+0.0015s)

Primality testing 5627^10304-10304^5627 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
5627^10304-10304^5627 is Fermat and Lucas PRP! (183.1293s+0.0024s)

To be completed...