Found with PFGW Version 3.6.0

197^5000-5000^197 is 2-PRP! (5.7751s+0.0017s)
197^5000-5000^197 is 3-PRP! (5.7078s+0.0018s)
197^5000-5000^197 is 5-PRP! (5.7182s+0.0017s)
197^5000-5000^197 is 7-PRP! (5.7122s+0.0035s)
197^5000-5000^197 is 11-PRP! (5.7005s+0.0035s)

Primality testing 197^5000-5000^197 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 14+sqrt(23)
Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.21% proof)
197^5000-5000^197 is Fermat and Lucas PRP! (33.8881s+0.0017s)

To be completed...