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Draw the diagram. You will notice that $\triangle MPF \sim \triangle GPH$ and $\triangle HNQ \sim \triangle FGQ$. 

Using the ratio of corresponding sides in these pairs of similar triangles, we have

$\dfrac{HQ}{QF} = \dfrac{2}{2 + 5} = \dfrac27$

and

$\dfrac{HP}{PF} = \dfrac{3 + 7}7 = \dfrac{10}7$

We suppose $HQ : QP : PF = 1 : a : b$ (if not, we just divide through the ratio until the first component is 1). 

Then,

$\begin{cases} \frac1{a + b} = \frac27\\ \frac{1+a}b = \frac{10}7 \end{cases}$

Cross-multiplying,

$\begin{cases} 2a + 2b = 7\\ -7a +10b = 7 \end{cases}$

Solving gives $a = \dfrac{28}{17}$ and $b = \dfrac{63}{34}$. Hence, $HQ : QP : PF = 34 : 56 : 63$.

In particular, $\dfrac{PQ}{FH} = \dfrac{56}{34 + 56 + 63} = \dfrac{56}{153}$.