Found with PFGW Version 3.7.5

5393^8366-8366^5393 is 2-PRP! (18.8894s+0.0015s)
5393^8366-8366^5393 is 3-PRP! (18.5909s+0.0017s)
5393^8366-8366^5393 is 5-PRP! (18.4451s+0.0017s)
5393^8366-8366^5393 is 7-PRP! (18.1855s+0.0016s)
5393^8366-8366^5393 is 11-PRP! (18.6302s+0.0016s)

Primality testing 5393^8366-8366^5393 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.08% proof)
5393^8366-8366^5393 is Fermat and Lucas PRP! (106.9050s+0.0026s)

To be completed...