CAPS 2019 Problem 2

We consider positive integers $n$ having at least six positive divisors. Let the positive divisors of $n$ be arranged in a sequence $(d_i)_{1\le i\le k}$ with $$1=d_1<d_2<\dots <d_k=n (k\ge 6).$$ Find all positive integers $n$ such that $$n=d_5^2+d_6^2.$$