Cosine of a Shifted Angle

Given $ \cos x = \frac{3}{5} $ with $ x $ in Quadrant I, what is the value of $ \cos\left(x - \frac{5\pi}{6}\right) $? The answer is in the form $\frac{a-\sqrt{b}}{c}$ where $a$, $b$, $c$ are positive integers, and $a+b+c$ is as small as possible. Input the value of $a+b+c$.