Found with PFGW Version 3.7.5

5035^7034-7034^5035 is 2-PRP! (21.5016s+0.0024s)
5035^7034-7034^5035 is 3-PRP! (22.3009s+0.0018s)
5035^7034-7034^5035 is 5-PRP! (25.0095s+0.0014s)
5035^7034-7034^5035 is 7-PRP! (27.4134s+0.0026s)
5035^7034-7034^5035 is 11-PRP! (26.9950s+0.0013s)

Primality testing 5035^7034-7034^5035 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)
5035^7034-7034^5035 is Fermat and Lucas PRP! (161.1883s+0.0040s)

To be completed...