Found with PFGW Version 3.7.5

5442^7289-7289^5442 is 2-PRP! (48.6337s+0.0071s)
5442^7289-7289^5442 is 3-PRP! (49.5465s+0.0070s)
5442^7289-7289^5442 is 5-PRP! (48.9294s+0.0090s)
5442^7289-7289^5442 is 7-PRP! (51.5792s+0.0087s)
5442^7289-7289^5442 is 11-PRP! (49.3395s+0.0096s)

Primality testing 5442^7289-7289^5442 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.09% proof)
5442^7289-7289^5442 is Fermat and Lucas PRP! (244.3567s+0.0056s)

To be completed...