Found with PFGW Version 3.6.0

5124^6869-6869^5124 is 2-PRP! (24.9283s+0.0028s)
5124^6869-6869^5124 is 3-PRP! (25.6946s+0.0047s)
5124^6869-6869^5124 is 5-PRP! (25.4616s+0.0039s)
5124^6869-6869^5124 is 7-PRP! (24.8924s+0.0024s)
5124^6869-6869^5124 is 11-PRP! (24.8689s+0.0027s)

Primality testing 5124^6869-6869^5124 [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 0.01% and helper 0.00% (0.05% proof)
5124^6869-6869^5124 is Fermat and Lucas PRP! (122.6645s+0.0034s)

To be completed...