Found with PFGW Version 3.7.5

4972^5535-5535^4972 is 2-PRP! (16.3962s+0.0041s)
4972^5535-5535^4972 is 3-PRP! (17.0939s+0.0027s)
4972^5535-5535^4972 is 5-PRP! (17.5657s+0.0029s)
4972^5535-5535^4972 is 7-PRP! (16.6265s+0.0026s)
4972^5535-5535^4972 is 11-PRP! (19.4163s+0.0028s)

Primality testing 4972^5535-5535^4972 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.17% proof)
4972^5535-5535^4972 is Fermat and Lucas PRP! (83.3440s+0.0051s)

To be completed...