Found with PFGW Version 3.6.0

5702^10071-10071^5702 is 2-PRP! (66.3020s+0.0038s)
5702^10071-10071^5702 is 3-PRP! (66.3813s+0.0034s)
5702^10071-10071^5702 is 5-PRP! (66.5827s+0.0023s)
5702^10071-10071^5702 is 7-PRP! (66.3877s+0.0022s)
5702^10071-10071^5702 is 11-PRP! (66.3692s+0.0021s)

Primality testing 5702^10071-10071^5702 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
5702^10071-10071^5702 is Fermat and Lucas PRP! (399.6611s+0.0048s)

To be completed...