Trig?

Well, there is a theorem stating that a line joining a midpoint of one side of a triangle and the centriod of the triangle has a measurement of $\frac {1}{3}$ of the measurement of the line joining the midpoint of the same side of the triangle and it's opposite vertex.

So, we get:

$\frac {x + 2}{5x - 3} = \frac {1}{3}$

$3x + 6 = 5x - 3$

$2x = 9$

$x = 4.5$

Getting the difference between AM and Gm, we get:

$5x - 3 - (x + 2) \Rightarrow 4x - 5 \Rightarrow 4(4.5) - 5 \Rightarrow 18 - 5 = \boxed {13}$

There.