Found with PFGW Version 3.7.5

5089^7440-7440^5089 is 2-PRP! (31.4385s+0.0034s)
5089^7440-7440^5089 is 3-PRP! (31.7197s+0.0031s)
5089^7440-7440^5089 is 5-PRP! (31.9022s+0.0033s)
5089^7440-7440^5089 is 7-PRP! (31.3756s+0.0034s)
5089^7440-7440^5089 is 11-PRP! (31.5626s+0.0031s)

Primality testing 5089^7440-7440^5089 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N-1 test using base 19
Running N+1 test using discriminant 37, base 12+sqrt(37)
Calling N-1 BLS with factored part 0.08% and helper 0.00% (0.24% proof)
5089^7440-7440^5089 is Fermat and Lucas PRP! (193.3757s+0.3588s)

To be completed...