DE-MO 2014 Problem 1

For which non-negative integers $n$ is $K=5^{2n+3} + 3^{n+3} \cdot 2^n$ prime?

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.