Found with PFGW Version 3.7.5

5037^9688-9688^5037 is 2-PRP! (23.7429s+0.0027s)
5037^9688-9688^5037 is 3-PRP! (23.5333s+0.0016s)
5037^9688-9688^5037 is 5-PRP! (24.5260s+0.0016s)
5037^9688-9688^5037 is 7-PRP! (23.1324s+0.0014s)
5037^9688-9688^5037 is 11-PRP! (23.1058s+0.0014s)

Primality testing 5037^9688-9688^5037 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
5037^9688-9688^5037 is Fermat and Lucas PRP! (115.0558s+0.0023s)

To be completed...