Found with PFGW Version 3.7.5

5955^10366-10366^5955 is 2-PRP! (33.7952s+0.0019s)
5955^10366-10366^5955 is 3-PRP! (34.3127s+0.0018s)
5955^10366-10366^5955 is 5-PRP! (34.5303s+0.0017s)
5955^10366-10366^5955 is 7-PRP! (34.0941s+0.0018s)
5955^10366-10366^5955 is 11-PRP! (33.7235s+0.0018s)

Primality testing 5955^10366-10366^5955 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
5955^10366-10366^5955 is Fermat and Lucas PRP! (166.7533s+0.0027s)

To be completed...