Found with PFGW Version 3.7.5

5970^7397-7397^5970 is 2-PRP! (44.4287s+0.0035s)
5970^7397-7397^5970 is 3-PRP! (46.3800s+0.0037s)
5970^7397-7397^5970 is 5-PRP! (51.6797s+0.0060s)
5970^7397-7397^5970 is 7-PRP! (45.9224s+0.0101s)
5970^7397-7397^5970 is 11-PRP! (46.1422s+0.0070s)

Primality testing 5970^7397-7397^5970 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.21% proof)
5970^7397-7397^5970 is Fermat and Lucas PRP! (275.5664s+0.0064s)

To be completed...