VN-TST 1992 Problem 5

Find all pair of positive integers $(x, y)$ satisfying the equation

$x^2 + y^2 - 5 \cdot x \cdot y + 5 = 0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.