【Analysis】For a proper fraction, when the difference between the numerator and the denominator is constant, the larger the denominator, the larger the fraction.
【Solution】Solution: $\frac{2007}{2009}<\frac{2008}{2010}, \frac{2008}{2010}<\frac{2009}{2011}, \frac{2009}{2011}<\frac{2010}{2012}$,
Therefore: $\frac{2007}{2009} \times \frac{2008}{2010}<\frac{2008}{2010} \times \frac{2009}{2011}<\frac{2009}{2011} \times \frac{2010}{2012}$,
That is $\frac{2007 \times 2008}{2009 \times 2010}<\frac{2008 \times 2009}{2010 \times 2011}<\frac{2009 \times 2010}{2011 \times 2012}$,
So, $a<b<c$
Therefore, the answer is: $C$.
5. (3 points) $a=\frac{2007 \times 2008}{2009 \times 2010}, b=\frac{2008 \times 2009}{2010 \times 2011}, c=\frac{2009 \times 2010}{2011 \times 2012}$, then we have ( )
A. $a>b>c$
B. $a>c>b$
C. $a<b<c$
D. $a<c<b$