Daedalos

Hello, I have to prove a case from a family of halting problems, where for given input x, the program will return False if program x halts on input 5^x and True otherwise. I know the general proof for halting problem, but in this case the dependant input makes it impossible to test halting program on itself. My attempt was to define a new function to eventually reach a contradiction: B is defined iff B is undefined. Unfortunately I got to different conclusion. Could you point me to the right direction, please? Thank you.