Found with PFGW Version 3.7.5

5228^7509-7509^5228 is 2-PRP! (33.4964s+0.0029s)
5228^7509-7509^5228 is 3-PRP! (32.8933s+0.0030s)
5228^7509-7509^5228 is 5-PRP! (32.3638s+0.0031s)
5228^7509-7509^5228 is 7-PRP! (31.9749s+0.0027s)
5228^7509-7509^5228 is 11-PRP! (32.4900s+0.0029s)

Primality testing 5228^7509-7509^5228 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
5228^7509-7509^5228 is Fermat and Lucas PRP! (164.8148s+0.0051s)

To be completed...