Found with PFGW Version 3.7.5

5581^7620-7620^5581 is 2-PRP! (31.4365s+0.0029s)
5581^7620-7620^5581 is 3-PRP! (32.7069s+0.0034s)
5581^7620-7620^5581 is 5-PRP! (28.6306s+0.0026s)
5581^7620-7620^5581 is 7-PRP! (32.5984s+0.0030s)
5581^7620-7620^5581 is 11-PRP! (33.4932s+0.0032s)

Primality testing 5581^7620-7620^5581 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 43
Running N+1 test using discriminant 61, base 20+sqrt(61)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.14% proof)
5581^7620-7620^5581 is Fermat and Lucas PRP! (169.0224s+0.0052s)

To be completed...