Evaluate and simplify the following complex fraction.
\[\Large\dfrac{ ~\frac {-5}{-2}~ }{ \frac{6}{7}} = \]
To simplify the complex fraction, we can begin by multiplying the numerator and denominator by the least common denominator of $-2$ and $7$, which is $14$. Multiplying the numerator and denominator by $14$ gives \begin{align*}
\dfrac{ \left(\frac{-5}{-2}\right)(14)~ }{ \left(\frac{6}{7}\right)(14) } &= \frac{-5\cdot 14}{-2\cdot 14} \div \frac{6\cdot 14}{7\cdot 14}\\
&=\frac{-5\cdot 14}{-2\cdot 14} \cdot \frac{7\cdot 14}{6\cdot 14}\\
&= \frac{(-5)\cdot (7)\cdot (14)\cdot (14)}{(-2)\cdot (6)\cdot (14)\cdot (14)}.
\end{align*}The $14\cdot 14$ terms cancel so we have \[ \frac{(-5)\cdot (7)}{(-2)\cdot (6)}.\]We can simplify further: \begin{align*}
\frac{(-5)\cdot (7)}{(-2)\cdot (6)} &= \frac{-35}{-12}.
\end{align*}Since the numerator and denominator are both negative, we can simplify even further: $$\frac{-35}{-12} = \boxed{\frac{35}{12}}.$$