Found with PFGW Version 3.7.5

5293^7488-7488^5293 is 2-PRP! (29.8718s+0.0023s)
5293^7488-7488^5293 is 3-PRP! (31.1920s+0.0026s)
5293^7488-7488^5293 is 5-PRP! (27.5212s+0.0024s)
5293^7488-7488^5293 is 7-PRP! (26.1887s+0.0023s)
5293^7488-7488^5293 is 11-PRP! (29.1612s+0.0025s)

Primality testing 5293^7488-7488^5293 [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 0.06% and helper 0.06% (0.24% proof)
5293^7488-7488^5293 is Fermat and Lucas PRP! (166.3875s+0.0050s)

To be completed...