Found with PFGW Version 3.7.5

5794^12105+12105^5794 is 2-PRP! (71.7138s+0.0030s)
5794^12105+12105^5794 is 3-PRP! (71.6682s+0.0033s)
5794^12105+12105^5794 is 5-PRP! (72.9591s+0.0040s)
5794^12105+12105^5794 is 7-PRP! (72.3749s+0.0029s)
5794^12105+12105^5794 is 11-PRP! (72.6615s+0.0042s)

Primality testing 5794^12105+12105^5794 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N-1 test using base 31
Running N-1 test using base 37
Running N+1 test using discriminant 43, base 2+sqrt(43)
Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.12% proof)
5794^12105+12105^5794 is Fermat and Lucas PRP! (593.8571s+0.0059s)

To be completed...