KöMaL 2014 C1212

Prove that $(2+3+5) \mid \big(2 \cdot 2^{5^3} + 3^{2^5} - 5^{3^2}\big)$ .

Official text KöMaL. 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.