Found with PFGW Version 3.7.5

5773^5826-5826^5773 is 2-PRP! (15.7469s+0.0031s)
5773^5826-5826^5773 is 3-PRP! (15.7430s+0.0028s)
5773^5826-5826^5773 is 5-PRP! (15.7163s+0.0029s)
5773^5826-5826^5773 is 7-PRP! (15.8148s+0.0026s)
5773^5826-5826^5773 is 11-PRP! (15.8999s+0.0025s)

Primality testing 5773^5826-5826^5773 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.12% proof)
5773^5826-5826^5773 is Fermat and Lucas PRP! (78.8803s+0.0044s)

To be completed...