Solve another Diophantine equation with 2 variables and odd degree 5

Question

See also the already solved question:

Solve a Diophantine equation with 2 variables and odd degree 5

Prove that there are no non trivial integer solutions to the equation $a^{5} -1 = 2b^{5}$

Answer 1

Let $a$ and $b$ satisfy $a^5 - 1 = 2b^5.$ Then $A = -a$ and $B = -b$ satisfies $A^5 + 1 = 2B^5.$ So by your previous question...