Found with PFGW Version 3.7.5

5784^9943-9943^5784 is 2-PRP! (25.9136s+0.0015s)
5784^9943-9943^5784 is 3-PRP! (25.9382s+0.0015s)
5784^9943-9943^5784 is 5-PRP! (25.9486s+0.0014s)
5784^9943-9943^5784 is 7-PRP! (26.0261s+0.0015s)
5784^9943-9943^5784 is 11-PRP! (26.4195s+0.0014s)

Primality testing 5784^9943-9943^5784 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.03% and helper 0.03% (0.12% proof)
5784^9943-9943^5784 is Fermat and Lucas PRP! (174.7569s+0.0024s)

To be completed...