Found with PFGW Version 3.6.0

5609^6804-6804^5609 is 2-PRP! (23.9805s+0.0026s)
5609^6804-6804^5609 is 3-PRP! (24.9748s+0.0038s)
5609^6804-6804^5609 is 5-PRP! (24.9083s+0.0042s)
5609^6804-6804^5609 is 7-PRP! (24.9427s+0.0040s)
5609^6804-6804^5609 is 11-PRP! (24.8715s+0.0042s)

Primality testing 5609^6804-6804^5609 [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 0.07% and helper 0.02% (0.23% proof)
5609^6804-6804^5609 is Fermat and Lucas PRP! (122.6272s+0.0041s)

To be completed...