Found with PFGW Version 3.7.5

5045^5226-5226^5045 is 2-PRP! (11.0353s+0.0101s)
5045^5226-5226^5045 is 3-PRP! (12.9583s+0.0009s)
5045^5226-5226^5045 is 5-PRP! (11.2140s+0.0014s)
5045^5226-5226^5045 is 7-PRP! (14.4708s+0.0056s)
5045^5226-5226^5045 is 11-PRP! (14.0222s+0.0010s)

Primality testing 5045^5226-5226^5045 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N+1 BLS with factored part 0.04% and helper 0.04% (0.17% proof)
5045^5226-5226^5045 is Fermat and Lucas PRP! (85.6944s+0.0030s)

To be completed...