Found with PFGW Version 3.7.5

5648^5943-5943^5648 is 2-PRP! (16.1351s+0.0020s)
5648^5943-5943^5648 is 3-PRP! (17.7675s+0.0027s)
5648^5943-5943^5648 is 5-PRP! (18.0711s+0.0022s)
5648^5943-5943^5648 is 7-PRP! (16.0583s+0.0021s)
5648^5943-5943^5648 is 11-PRP! (16.9977s+0.0026s)

Primality testing 5648^5943-5943^5648 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.08% and helper 0.03% (0.27% proof)
5648^5943-5943^5648 is Fermat and Lucas PRP! (103.0345s+0.0047s)

To be completed...