Found with PFGW Version 3.7.5

5744^7035-7035^5744 is 2-PRP! (26.3468s+0.0024s)
5744^7035-7035^5744 is 3-PRP! (26.2177s+0.0033s)
5744^7035-7035^5744 is 5-PRP! (29.4948s+0.0026s)
5744^7035-7035^5744 is 7-PRP! (32.6616s+0.0032s)
5744^7035-7035^5744 is 11-PRP! (32.3926s+0.0032s)

Primality testing 5744^7035-7035^5744 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.22% proof)
5744^7035-7035^5744 is Fermat and Lucas PRP! (156.3468s+0.0064s)

To be completed...