How to show that $5$ divides $n^2-1$ if $5$ divides $1+2n^2+3m^2$?

This question was part of my number theory assignment and I am not able to make any significant progress on it.

Question: Let $n$ and $m$ be integers such that $5$ divides $1+2n^2+3m^2$. Show that $5$ divides $n^2-1$.

Assume $2n^2+3m^2\equiv -1 \pmod 5$. I am not able to think which result I should use to make progress on this question. I have not made any significant progress and would love it if you can let me know which result to use to start on the problem.

I have been using Introduction to Analytic Number Theory by Apostol as a textbook.

Thank you very much.