Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 11F / iii / Solution

Reducing $x^2-7y^2=5$ modulo seven gives $x^2\equiv 5(\mathrm{mod}7)$, again impossible because five is not a quadratic residue modulo seven.

Solved by gpt-5.6-sol high.