Found with PFGW Version 3.7.5

5330^9589-9589^5330 is 2-PRP! (23.6091s+0.0014s)
5330^9589-9589^5330 is 3-PRP! (23.1060s+0.0015s)
5330^9589-9589^5330 is 5-PRP! (23.5385s+0.0015s)
5330^9589-9589^5330 is 7-PRP! (23.0331s+0.0016s)
5330^9589-9589^5330 is 11-PRP! (23.2285s+0.0016s)

Primality testing 5330^9589-9589^5330 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
5330^9589-9589^5330 is Fermat and Lucas PRP! (116.7429s+0.0022s)

To be completed...