Show that a cubic Diophantine equation has no solutions

Question

Show that the Diophantine equation $x^3+117y^3 = 5$ has no solutions.

I tried using like an odd and even argument for $x$ but it doesn't seem to work because it doesn't matter if $x$ is odd or even. Any help would be great.

Answer 1

Hint: The cubes modulo $9$ are $0$, $1$, and $-1$.