AMC 12A 2014 Problem 22

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} ?

Answer Choices
A. 278
B. 279
C. 280
D. 281
E. 282