Found with PFGW Version 3.7.5

5892^7147-7147^5892 is 2-PRP! (46.6186s+0.0070s)
5892^7147-7147^5892 is 3-PRP! (46.4170s+0.0062s)
5892^7147-7147^5892 is 5-PRP! (46.3203s+0.0079s)
5892^7147-7147^5892 is 7-PRP! (46.5112s+0.0073s)
5892^7147-7147^5892 is 11-PRP! (45.9673s+0.0073s)

Primality testing 5892^7147-7147^5892 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.13% proof)
5892^7147-7147^5892 is Fermat and Lucas PRP! (227.2730s+0.0058s)

To be completed...