Found with PFGW Version 3.7.5

5027^5966-5966^5027 is 2-PRP! (17.1508s+0.0019s)
5027^5966-5966^5027 is 3-PRP! (16.7073s+0.0022s)
5027^5966-5966^5027 is 5-PRP! (19.3966s+0.0033s)
5027^5966-5966^5027 is 7-PRP! (21.4233s+0.0035s)
5027^5966-5966^5027 is 11-PRP! (21.3347s+0.0044s)

Primality testing 5027^5966-5966^5027 [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 0.04% and helper 0.03% (0.16% proof)
5027^5966-5966^5027 is Fermat and Lucas PRP! (108.6142s+0.0045s)

To be completed...