Found with PFGW Version 3.5.2

79^5319+78 is 2-PRP! (3.1568s+0.0046s)
79^5319+78 is 3-PRP! (3.0625s+0.0009s)
79^5319+78 is 5-PRP! (4.0428s+0.0009s)
79^5319+78 is 7-PRP! (4.9511s+0.0009s)
79^5319+78 is 11-PRP! (6.0778s+0.0009s)

Primality testing 79^5319+78 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N+1 BLS with factored part 0.11% and helper 0.04% (0.38% proof)
79^5319+78 is Fermat and Lucas PRP! (19.2346s+0.0042s)

To be completed...