Found with PFGW Version 3.7.5

5505^8008-8008^5505 is 2-PRP! (24.9564s+0.0023s)
5505^8008-8008^5505 is 3-PRP! (25.2735s+0.0023s)
5505^8008-8008^5505 is 5-PRP! (24.8490s+0.0021s)
5505^8008-8008^5505 is 7-PRP! (24.9543s+0.0022s)
5505^8008-8008^5505 is 11-PRP! (25.4811s+0.0022s)

Primality testing 5505^8008-8008^5505 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 41, base 1+sqrt(41)
Calling N-1 BLS with factored part 0.07% and helper 0.00% (0.20% proof)
5505^8008-8008^5505 is Fermat and Lucas PRP! (129.3829s+0.0037s)

To be completed...