Found with PFGW Version 3.6.0

5922^6791-6791^5922 is 2-PRP! (25.0002s+0.0029s)
5922^6791-6791^5922 is 3-PRP! (25.1030s+0.0047s)
5922^6791-6791^5922 is 5-PRP! (25.0355s+0.0046s)
5922^6791-6791^5922 is 7-PRP! (25.1142s+0.0051s)
5922^6791-6791^5922 is 11-PRP! (25.1048s+0.0043s)

Primality testing 5922^6791-6791^5922 [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 0.03% and helper 0.01% (0.10% proof)
5922^6791-6791^5922 is Fermat and Lucas PRP! (122.9249s+0.0038s)

To be completed...