2014 AMC 10A Question 25

The number $5^{867}$ is between $2^{2013}$ and $2^{2014}.$ How many pairs of integers $(m,n)$ are there such that $1\leq m\leq 2012$ and $$
5^n < 2^m < 2^{m+2} < 5^{n+1}?
$$