Found with PFGW Version 3.7.5

5123^7284-7284^5123 is 2-PRP! (49.9390s+0.0084s)
5123^7284-7284^5123 is 3-PRP! (49.9874s+0.0069s)
5123^7284-7284^5123 is 5-PRP! (47.4410s+0.0063s)
5123^7284-7284^5123 is 7-PRP! (52.3452s+0.0064s)
5123^7284-7284^5123 is 11-PRP! (49.0974s+0.0055s)

Primality testing 5123^7284-7284^5123 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.07% and helper 0.03% (0.25% proof)
5123^7284-7284^5123 is Fermat and Lucas PRP! (246.6112s+0.0053s)

To be completed...