Let $N=3^{1000}\times 2^{200009} +1$. Show that $5^{\frac{N-1}{2}}\equiv -1 \pmod{N}$.

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This is showing that 5 is a quadratic non-residue mod N but I don't get why this says it is prime.

The question also asks that you say that if p was prime divisor of N what the power of 2 dividing $ord_{p}(5)$ could mean and how to use that to conclude that all divisors p of N are $\equiv 1 \pmod{2^{2000009}}$. Not sure what the relevance of the the order is.

Any help is appreciated.