Found with PFGW Version 3.7.5

4967^5928-5928^4967 is 2-PRP! (15.5206s+0.0021s)
4967^5928-5928^4967 is 3-PRP! (16.5133s+0.0026s)
4967^5928-5928^4967 is 5-PRP! (17.5878s+0.0020s)
4967^5928-5928^4967 is 7-PRP! (15.6166s+0.0018s)
4967^5928-5928^4967 is 11-PRP! (17.5762s+0.0023s)

Primality testing 4967^5928-5928^4967 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 31
Running N-1 test using base 43
Running N-1 test using base 47
Running N-1 test using base 59
Running N+1 test using discriminant 67, base 6+sqrt(67)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.16% proof)
4967^5928-5928^4967 is Fermat and Lucas PRP! (176.5200s+0.0035s)

To be completed...