Found with PFGW Version 3.8.0

5175^11096-11096^5175 is 2-PRP! (34.8597s+0.0065s)
5175^11096-11096^5175 is 3-PRP! (35.0597s+0.0072s)
5175^11096-11096^5175 is 5-PRP! (35.2423s+0.0065s)
5175^11096-11096^5175 is 7-PRP! (36.5943s+0.0070s)
5175^11096-11096^5175 is 11-PRP! (34.7135s+0.0072s)

Primality testing 5175^11096-11096^5175 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
5175^11096-11096^5175 is Fermat and Lucas PRP! (171.6573s+0.0057s)

To be completed...